Unclear ending?

I used a KIA type of structure as white here and the position seemed to be unbalanced most of the time. I've got to say I  was a bit shocked by his 33...Rxg2+, sacrificing the rook for bishop and two pawns! I got really scared by those 3 passers, although after the game the engine told me I was better the whole time. I played Ra7, with the idea Re7 to draw by perpetual. My opponent, trying to avoid Re7, probably thinking he had good chances to win, missed a mate in one! I got lucky! But before that blunder, what plans would you suggest for both sides. Is perpetual my best shot? Or did I have a win? The game was 15|10.

36...Bb7 37. Re7 Bxg2 and maybe black can avoid mate threats unless white does a king walk. But white can't possibly lose since there's at least a perpetual.