The From's Gambit might be worth trying as well, although most Bird players are likely to know their stuff there.
I squashed a Bird, but then it flew away
49 g5 was a bone-headed move on your opponent's part. After 49 h5 (to secure the pawns on the Kingside so that no breakthrough there is possible), White can give up the b-pawn and still keep Black from making progress. It's even possible to win some lines if Black isn't careful.
52 ... g4 actually loses for you, and all of your pawns are what spells your downfall. You're correct that 52... e4 is the only way to win. Here's what happens after 52 ... g4 (diagram included):
52 ... g4??
As shown in the diagram, 52 ... e4 is the road to a win.
53 Kd5 g3
54 d7! Kd7
Else White promotes with check and stops Black from promoting.
55 Ke6 g2
55 ... Kd8 instead is covered in the diagram. On other moves than that and the given move, White will promote first.
56 Ke7!
The less flashy 56 b7+ also works, but it's much slower.
56 ... g1=Q
Black promotes first, but to no avail.
57 d8=Q+ Kb7
58 Qd7+ Kb6
Or 58 ... Ka8, which speeds the process up.
59 Qc6+ Ka7
Or 59 ... Ka5, 60 Qa6#.
60 Qc7+ Ka8
61 b6!
The point. Black's King is cornered (literally), and the Queen has no way to get to a square that defends against Qa7# or Qc8#.
61 ... Qg4+
62 Ke8
Black's Queen is out of useful checks, and his wealth of pawns are in his Queen's way. Mate follows shortly.
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I started this tournament with 0.5 out of 4 possible then I won a game with someone rather weak. I knew this opponent likes to play the reversed Stonewall and I knew I would really need to win (to get the best under 1600 prize). It turns out he played an Ilyin-Genevsky system instead. watch what happened.
just a sec, forgot to put in the game. instructive pawn endgame in my little opinion.