lost a won game; where did I go wrong?


61. ... Kb6? 61. ... Kd6 is a simple draw.
64. ... Kb8?? 64. ... Kb7 is a draw.
44. ... g3+. This just weakens the pawn. Unless you have a concrete idea, there's no reason to separate this pawn from it's protection yet. Why not just 44. ... Rf3+ followed by 44. ... Rxf4.
When you are up in material, trade pieces. At move 39, when white play f4, you could have responded with gxf4. If you did that, you would not need to deal with the passed pawn.
Hope this help :)

trade pieces but not necessarily pawns
if you get to pawn ending your just winning very easily 2 vs 4 pawns

You may even still be fine after 44. ... g3+
Instead of 45. ... Rh5, how about
45. ... g2
46. Rg1 Rh1
47. Kf2
You are a move up on the game line and you can play
47. ... Be4
48. Bxe4 Rxg1
49. Kxg1 fxe4
And your king can catch white's f-pawn leaving you a pawn up in a king and pawn ending. I certainly wouldn't want to go into this line unless I had to. Being patient and not pushing g3 until you know it's winning is better.

I think I was in time trouble by move 47, with about 30 seconds left(and 5 second increments to sustain that 30 seconds) but I still should have won the king and pawn ending

I think the king and pawn ending is a draw. But you could have played it better, giving your opponent the opportunities to lose it instead of the other way around.
60. ... d3
61. Kxd3 Kd5
62. Kc3 Ke4
63. Kc2 Kd4
63. Kb3 Kd3 etc.
Black can win the white b-pawn. When black plays Kxb4 white has to play Kb2 for the draw. This is the same idea that you missed to lose the game on your end. You could have put the same challenge to your opponent instead of the other way around.