Additional lands doesn't make the D4s weaker. In the example you described there are still 53 cards left in the deck. That means you don't have resources yet. You have to build a grind board state to actually start grinding. If you get lucky with the first D4, then you should go as deep as you want (and kill if you can or play Belcher pass), but it doesn't guarantee that you'll get the kill because you dilute the main deck to an anti-control version that prefers consistency, perpetual resources, and protection. These things naturally inhibit long spell chains no matter what board configuration of the grind plan that you play. Its better to first secure a board state, then grind out the win. In the case of having multiple LGs in hand, they are not necessarily guaranteed land drops. Your opponent can Snare or Pierce them knowing that eventually you'll have enough land to negate the Pierce/Daze. Having extra lands means you get to turn off Spell Pierce and Daze and force them to play hard counter magic on your business. In that case lands become valuable and actually lets you resolve your D4s instead of trading D4 for Spell Pierce until they run out of counter magic. The more of them you draw the better and the more of them you play the better chance you have of opening with one or two. Ideally, I prefer to open with 3 perpetual resources and work up from there. If I add in some acceleration, we can dodge Pierce/Daze with the rituals or CoF and force them to FoW/Counterspell. Once the hard counter magic is gone, you can play your Belcher or IT and get there.
Granted, having more lands means that you are almost guaranteed to misfire if Belcher comes down early. But when we know we are moving to mid game if we don't get off an early protected business spell, Carpet vs. slower control, or early EtW, then it doesn't matter that you are playing 5 lands in a deck that plays Belcher because you often play at least 3 of your lands while grinding. By the time Belcher comes down, you have a lower chance of misfiring, especially if you leave Taiga for last because you haven't gone for EtW already. Otherwise, when Belcher comes down early.. decks like RUG/UR Tempo have absolutely no way to remove Belcher and Miracles/Stoneblade don't often remove it either, and when the have, I'm so far ahead with perpetuals that they lose anyway. This isn't always the case but too often does an early Belcher win the game even through 2 or 3 misfires while a mid or late game Belcher means I've already hit all my lands or most of them. Keep in mind that in testing of this build with much land, I haven't actually lost because of Belcher misfires. Most of the time I've lost because I don't have enough perpetual resources to grind effectively.
I'm not a fan of PIF because the only cards it works well with post-board are D4s, IT, Crit, Drit, EtW, and Tendrils. Pact and Culling come out so you won't always have shit sitting in the yard to abuse when you draw it as a potential business spell. Further, Carpet and LED do not work with PIF at all but you can actually use either one with IGG. I've won the game by returning a countered Carpet of Flowers with a Bayou to cast, pass to second main phase and add enough mana to get there. Also, IGG is fantastic with LED, unlike PIF. You can't IGG loop if LED is your acceleration for PIF. Thats huge especially if your meta has a lot of combo where you need the win right now and can't just go for tokens. Against blue though where PIF > IGG.. EtW is just as effective as PIF but for the cost of 3R vs. 3R + B initial mana source. Also, IGG has been indispensable in the discard match ups. Also, I don't know how often you've encountered IGG as business spell but it can be a pseudo-mind twist. SI has a much easier time recovering form "discard 4 cards" than most other decks. In general I've found IGG to be much more flexible even though its not a card I can port to the control match ups, where main deck PIF would be. Granted each has there own play style so if it works, go for it but I haven't had much luck with it myself in the main deck. I'm more optimistic about putting it in the sideboard. I might cut a Bayou for it.
Also, if you find yourself having trouble against Maverick or DnT because of Thalia, have you considered having the main deck EtW and 3 EtW in the board? It makes your spell chains smaller so you can D4 into Belcher, pass the turn or EtW pass.. or just natural EtW from your hand via Taiga or Lotus Petal. 10 tokens gets there if its turn 1. I find it more consistent to go for tokens then hope you have the piece of hate and they don't also drop Mother of Runes, or force you into a must win situation after you remove the bear. The EtW are also indispensable in the Tempo matchup where 4 EtW gives you a higher chance of opening T1 with tokens and just steam rolling them.. especially when the grind plan is less effective against Tempo due to needing fewer Islands to function, Daze, a faster clock, and reach.
If you want to abuse PIF to its fullest potential, perhaps a Belcherless Pact list, with post-board PIF and Lands would be the best bet. Tendrils and EtW in the main deck.
So, off the top of my head.
maindeck PIF and then:
SB
4 Duress
4 Carpet of Flowers
2 EtW
1 PIF
3 Bayou
1 Taiga
So you'll have 2 PIF 3 EtW afterwards and you'll be going for a longer spell chain or hoping to hit EtW on a single D4. You won't have to worry about Belcher misfire at all, lands will help facilitate a PIF line of play, same as CoF. I wonder if some variation of this could work for PSI. Its more vulnerable to Flusterstorm (no Belcher), and it relies on longer spell chains, and its very graveyard hate able if they catch on and board in their Crypts, Relics, etc. though I think I'll test it anyway and see how it goes. That is, after I've tested the 4 land SB plan I'm running currently against various Tempo decks. I've concluded its pretty damn good against slower controls decks. The tempo matchup is still largely untested.
As far as the man plan goes, Death's Shadow actually isn't that bad. I used to play 2 in the main deck actually and they were occasionally really awesome, especially when I boarded into the full man plan. Its definitely a strictly Tempo meta strategy though. STP and Snapcaster rape the man plan otherwise.