After Be4?? it was a dead draw, but I suppose you already knew that. But, I think despite the material advantage for White, he will have an extremely difficult time making a win out of the position even after 44. Rxd3!. The plan would be to try and win the g-pawn, which would first require removing Black's king then moving in with your Rook or King. This would probably take an extremely long time, honestly, I don't see a clear way to do it.

So barring mistakes, White has a tough time to win (but it's probably still doable) after 44. Rxd3.

I don't think I'd have problems winning the g pawn after 53. Bf5, the problem then however would be keeping the h pawn and avoiding the rook checks at the same time.

35. Bxf5 would of made the endgame more easily winnable for me, since the a pawn wasn't going anywhere as long as the bishop defended b1.

*sigh* I guess I have to accept I have a hard time finding good moves if I'm not fully concentrated.