Ok, but then we have to assume that he's playing the Cage (which he probably is), AND that he has it to play Turn 1.
Based on what I've read and done some solitaire with, I'm of the impression that if the opponent doesn't have the Cage by Turn 2 (draw)/Turn 3 (play), he's not going to be able to hate on the yard because by that point we should be going off.
Let's say he does have it Turn 1 and he's on the play. I can imagine our turns to be something like this:
Turn 1 -- Draw, play land, play P. Imp, discard dredger, done.
Turn 2 -- Draw, play land, play Breakthrough for 1, draw 4, then either A)discard all except Grudge/Claim/whatever and hold it for next turn or B)discard all except dredger, then discard dredger to pump Imp. Either way, swing with Imp and pass turn. (I may even keep the dredger in hand to bluff)
Turn 3 -- This is where it could start to get hairy because we don't have any cards in hand unless we were able to keep a card to eliminate the Cage.

