I've been developing this deck lately and it seems to be working reasonably well in testing, at least enough that I took the time to make an account and share it with the forum for feedback. I'm sure other people have thought of it before but I didn't find much discussion when searching for it.

Currently my deck looks like this:

4 Taiga
4 Wooded Foothills
1 Forest
4 Elvish Spirit Guide
4 Simian Spirit Guide
4 Tinder Wall
1 Akroma, Angel of Fury
4 Burning Wish
4 Gitaxian Probe
4 Rite of Flame
2 Desperate Ritual
4 Manamorphose
1 Traverse the Ulvenwald
4 Seething Song
4 Carnage Tyrant
4 Lotus Petal
4 Orcish Lumberjack
3 Empty the Warrens

SB: 1 Empty the Warrens
SB: 1 Past in Flames
SB: 3 Pyroblast
SB: 1 Red Elemental Blast
SB: 1 Shattering Spree
SB: 1 Tendrils of Agony
SB: 3 Surgical Extraction
SB: 1 Goblin War Strike
SB: 1 Grapeshot
SB: 1 Reforge the Soul
SB: 1 Cave-In

It's basically a belcher-esque shell that trades off the 'all-in' elements for fatties that are hard to interact with. When I say 'hard to interact with', I mean: can't counter, can't easily remove, and preferably has some sort of evasion so it isn't easily stalled out or chump blocked. The number of such fatties is surprisingly limited and relatively clunky (stuff like Thrun, the Last Troll or Akroma, Angel of Fury), but Ixalan has recently blessed the format with what I believe to be an underrated card: Carnage Tyrant. The idea struck me when Arianrhod was interviewed after beating Storm during Eternal Weekend and remarked how there is nothing that can currently deal with the giant Dino in the current (very fair) meta. (Yes, edict effects and sweepers exist - more on that in a moment) Since being six mana makes it relatively castable with acceleration, and storm-generated hordes of goblins have traditionally also been an acceleration-based strategy that's hard to interact with, and Green/Red are prime colors for fast acceleration, AND there's an existing shell using all that stuff that's been proven to be viable... for all these reasons I got motivated to take a stock Belcher deck, rework its manabase and change its threats, so at the end I present to you: Dino Storm.

From testing, the deck is consistently able to push 7-14 power on the board in the first two turns, all the while ignoring counters, spot removal and most permanents the meta currently throws at it. Combo decks have felt to be a bit of a coin toss though as you have to race them and the game is basically decided in advance by your opening hand. Nevertheless, the sideboard offers interesting options so that you can simply side out the threats that are not appropriate/too slow and replace them with faster or more controllish elements if need be. As for the inevitable 'why are you not just playing Storm/Reanimator/Show and Tell/Belcher' objection to the deck, I'd say first that this is obviously a good question to which there may very well be no answer (in other words, the deck is probably just bad and you can safely ignore the thread), but if one were to put more faith in this brew, you could argue that it is:
-Less vulnerable to post-board hate than Storm or Reanimator
-More resilient and less all-in than Belcher
-Harder to interact with and more threat-dense than Show and Tell. I don't know the exact numbers, but SnT decks currently run something like 8-10 threats (depending on whether it's a omnitell/pure sneak and show/hybrid build etc. correct me on that) and 8 enablers. Dino Storm runs at 11+ threats (at the very least 4 Dinos + 3 Empty the Warrens + 4 Burning Wish) and there is no need for an enabler, or more accurately the remainder of the deck is an enabler. Sure the payoff isn't as comparable as the flying demon/tentacle monster/ant swarm can be, but the need for enablers is much less strict - eventually you will just hardcast your fatty, whereas Sneak and Show isn't doing anything as long as it hasn't resolved one of its mainsake cards. I'm more detailed on this objection because I think it is the most valid - there is a very real chance that hardcasting dinos is just a worse SnT strategy, but it can't hurt to try brewing.

Some explanations about the card choices:

11 Land - I found that I want to draw one or two over the course of a game, rarely more. Since basically half the deck is focused on making mana any land beyond the third would feel awfully redundant. Taigas and fetches that get taigas are pretty explanatory here, but I added a single Forest so I can get a reliable green source that doesn't get wastelanded during opp's T2, plus it's fodder for Orcish Lumberjack. Green mana is sometimes hard to come by when most of the acceleration comes in red. In any case the manabase is far from optimized but I haven't reached the point where I need to tweak land counts and fetch names.

4 Carnage Tyrant - Pretty explanatory, if the card weren't printed I wouldn't have made this thread. As was said earlier, there is very little that can currently deal with the giant dino - basically Council's Judgement, sweepers and edict effects. It ignores most taxing effects (Thalia, Guardian of Thraben, Thorn of Amethyst, Trinisphere). Stonewalling it isn't an option, either - it laughably tramples over True-Name Nemesis, Tarmogoyf, Batterskull, Mirran Crusader (with or without mom), Gurmag Angler, most Eldrazi up to Endbringer... I could go on. Amusingly it even trades with Griselbrand (!!!). Baleful Strix can be an issue, but even then they still have to take six. There is a sort of infantile, almost regressive Timmy-like pleasure in slamming the big lizard in the face of all the hyper-efficient blue meta: I want to play my upgraded Craw Wurm - you can't say 'no', can't say 'but', can't say 'if'. It's gonna resolve, it's gonna stick, and boy it's gonna swing.

1 Akroma, Angel of Fury - Basically Carnage Tyrant #5. I wanted something that ignores permission and most removal and she seemed like a good idea, until I encountered my first Karakas in testing... I first started with 4, then gradually trimmed her to 1 and am considering cutting her completely. 8 mana is a lot, even with a morph ability, and the additional vulnerability to Karakas doesn't help. Being able to blank Delver and Flickerwisps is nice though.

3 Empty the Warrens and 4 Burning Wish - The usual business spells when you run a deck with a lot of acceleration. Being able to go wide as well as big is an important draw to the deck: too often would my opponent encounter a goblin hordes G1, side in Ethersworn Canonists/Flusterstorms, then stare at a huge reptile G2... the other way around is even more hilarious: you power out your uncounterable dinosaur, your opponent goes like 'wtf' and can't do anything G1, they side out counters for edict effects and the like, and G2 you just storm them out. Depending on the matchup I would sometimes side out/side in an entire half of the threat base between games - the psychological element is real. It's akin to the dilemma when you resolve Show and Tell and your opp has to decide between slamming Ashen Rider or Trinisphere... it's not a great place to be.

4 Seething Song, 4 Lotus Petal, 4 Rite of Flame, 4 Elvish Spirit Guide, 4 Simian Spirit Guide, 2 Desperate Ritual- Standard acceleration package. Guides are great for Daze blowouts. Petals provide an important source of color fix for Dinos or when you have to go for the Tendrils kill. I cut on the number of Desperates because they are the weaker acceleration spell and I need the slots.

4 Gitaxian Probe, 4 Manamorphose - Probe is obviously very good at cycling through your deck, adding storm, seeing if the coast is clear for a Burning Wish, etc. I keep 4 copies of Manamorphose because the manafix is often needed: green sources are essential for the dinos, and sometimes you need black for Tendrils.

4 Orcish Lumberjack, 4 Tinder Wall - The fastest manadorks in the format. Orcish Lumberjack is essential for powering out good and resilient T2s. A savvy opponent will try to counter the acceleration spell chain when they see they can't counter the haymaker, but very rarely will they counter the Orc - and when it's on the board you hardly need a spell chain to power out the six mana monster. Also, orc + tapping the forest that's sacrificed means 4 mana at the very least, so Empty is basically guaranteed and any additional acceleration is just gravy for more storm count. Tinder Wall is another very fast dork that can generate mana right away. It's also a very decent blocker if you find yourself having to race. Note that mana dorks also protect you from edict effects. When it doesn't come down along with a bunch of Goblins, the dino is often found with its orcish buddy ready to sacrifice itself to these nasty Lilianas.

1 Traverse the Ulvenwald - A flex slot I'm testing, as with Akroma I started out with 4 and found myself cutting down to 1. It sometimes acts as a forest finder in times of emergency but most of the time it's basically a Green Sun's Zenith that doesn't use up all your mana, so if your opponent counters that you can still use the mana for something else. Delirium is reasonably easy to achieve between all the lands you sacrifice, instant/sorceries in the acceleration package, petals and tinder walls. The problem is I have often found myself in situations where I exposed myself too much in trying to achieve Delirium, e.g. I generate way more mana than I need with Seething Song and Tinder Wall and that goes to waste if the Traverse gets countered. For these reasons I kept trimming it but I still keep a copy around to maximize threat density.

Now the sideboard is much wilder, I don't know exactly what I'm doing and I'm sure there's room for a lot of flexibility.
Empty the Warrens - Classical wish target
Past in Flames - Another wish target inspired from the monored storm builds, but I haven't found a usecase for it yet in testing.
Pyroblast and Red Elemental Blast - I often found I had extra red mana from all the acceleration and being able to fight to resolve a wish is nice. It's also good versus Show and Tell. Generally speaking you can't go wrong when a card reads 'R: Counterspell/Vindicate' against a large swath of the format.
Shattering Spree - Chalice, Ethersworn and Trinisphere aren't as annoying as they can be to Storm decks but sometime you just need to get them off the board. Could be replaced by By Force, I don't know.
Tendrils of Agony - I know this is clunky when you only have 4 Manamorphose and 4 Lotus Petal to cast it but there are a number of permanents against which the deck simply can't win without this card: Glacial Chasm, Moat, Blazing Archon, Elesh Norn, etc. Sometimes they stabilize and the board gets stalled and you only need to deliver the final life loss. Sometimes you know they are going to kill you next turn if you don't kill them on your turn. The Tendrils kill provides an out for too many situations at too small a cost (one slot) not to be included.
Grapeshot - Untested for now, I guess it provides an alternative for Tendrils when you can't make black mana. Remember you often eating up large chunks of your opponent's life total in the very first turns so the needed storm count isn't as high as it appears.
Surgical Extraction - A very versatile card against many decks, can't really go wrong with this.
Goblin War Strike - When you've made an early horde and need to deliver the last strike before they kill you, or when you've made a huge horde and can just one-shot them. More testing needed.
Reforge the Soul - Seeing how the deck has next to no CA but provides many ways to make mana I thought about testing this card. Obviously it's not as good against Force of Will decks but the whole point of this deck is that your threats ignore permission. More testing needed.
Cave-In - Mostly a concession to elves and other matchups with lots of annoying weenies. Also relevant against Elemental or Monk armies that can eventually pile up to multiple-block your dinos.

Cards I've thought about:

Thrun, the Last Troll - Although solid at first glance, it got outclassed by a lot of creatures recently. Gurmag, Batterskull, Reality Smasher, Endbringer, True Name, Crusader... it also gets chump blocked to oblivion by Mom-backed blockers, Wirewood trickery or Elemental tokens.
Altered Ego - Being able to copy your dinos seems nice although it sounds win-more to me. Being able to copy your opp's fatties on the other hand sounds hilarious enough that I'll probably get around to testing this card. I'm not a fond of the blue splash though, makes the manabase even shakier.
Hunting Pack - Last I heard 4/4 are stronger than 1/1s. However there's probably a reason this card currently doesn't see play in any storm shell. Maybe it fits well this shell, only testing can tell.
Street Wraith - I first tried these for more deck thinning and delirium enabling, but I mostly just cut them for 'real' cards. The life loss isn't trivial with probes and mulligan decisions are already hard enough in a deck with no selection.
Lion's Eye Diamond - Awkward with a Dino or Empty in hand. Awkward when you Wish, crack LED in response, only to see it get countered. So much for a deck that tries to ignore permission.
Faithless Looting - Card disadvantage, not great against opposing deathrites, makes the deck slower... maybe in a graveyard-centric shell? I don't know.
Chandra, Torch of Defiance - Although it does get countered I have often found in my days of playing Dragon Stompy and Monored Sneak Attack that many decks have no way to handle a resolved Chandra t1 or even t2. She also fits nicely with the gameplan, providing acceleration, control (gotta kill those pesky lilianas and strixes), CA and a wincon in one card. She probably deserves some testing in the sideboard. If testing finds that there are too few threats and too much mana in the deck I'll try a copy maindeck.
Volcanic Fallout - There aren't so many blue decks that go wide that this should replace Cave-In, but in some metas it can be relevant.

I can't post matchups yet because the deck is still very much in construction and I didn't test enough yet to get a firm grasp of the matchups, but I will try to detail them more as the experiment progresses and the deck shows promises (or not).

Any feedback is appreciated. You are encouraged to test the deck, it's very fun to play and provides many angles of attack so you never tire of playing the same strategy over and over again. The sideboard tactics can be entertaining as well if that's your sort of thing. In any case, thank you for taking the time to read all this if you've made it this far.