30...H(8,9)
Chess on an Infinite Plane (game: cobra91 - vickalan)
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31. R(8,10)
31...N(6,8)
Very clever! White must now give up his best pieces.
32. R(5,9)x(8,9)
Too bad I lost my hawk.
It will be interesting to see if this game goes far enough where the other hawks get put into play, or if it will be decided before that.
32...Nx(8,9)
Oh, I expect this to go at least 30-50 more moves, unless an enormous mistake is made. I've played a few large-board variants in the past (though never an infinite-board variant), and they take ages to play through to completion.
Fittingly enough, our other game might last almost as long, because (I think) you missed a couple of chances to finish the game off a lot sooner. I suspect White can now fight that one out for some 2-3 dozen extra moves.
Since there's no real choice, I'll continue by trading off my other strong piece:
33. Bx(8,7)+
I see it as both games going for dozens of moves also. I was mainly wondering if me not having a hawk anymore to fight or defend my backside pawns will play a role later in the game. Probably too hard to know for sure. Since the pawns and hawks are somewhat slow-movers, I can envision some games where they might not be used at all, or aren't used until someone tries to promote some pawns near the end of a game. And you're right - that can be very far from the position we have now.
33...Kx(8,7)
Yes, it should be quite some time before the "background pawns" become viable targets, because their current value is so small (compared with the "main pawns", for instance), and they are far away from the most important areas of the board. The hawks will enter play much sooner, though - probably within the next 5-10 moves.
34. Rx(-1,10)
34...C(3,8)
35. B(1,3)
...And so begins the long and tedious maneuvering phase. 
It's interesting that only one pawn has been lost so far, and both our pawn structures are still in pretty good shape (no doubled pawns, isolated pawns, etc.). i.e. in this respect both white and black still have considerable strength.
35...(-2,11)
I agree. In some ways, this now resembles a few of the large-board variants I've previously tried. The main difference is that play is "freer" here, with limitless space for development and expansion in all directions.
36. R(8,10)
36...K(9,8)
37. C(-4,9)
37...C(8,8)
38. C(7,9)+
38...K(9,9)
39. C(8,11)+
30. R(14,10)