How to fail to use a winning advantage

This game was a huge disappointment for me, it's really shaken my confidence. I attained what I believe was a winning advantage (central connected passed pawns) after some heavy queenside maneuvering, but somehow lost it and ended up in a drawn position. Can anyone with better endgame skills show me where I went wrong? I think I know of one place, it's in the notes. Also, did I actually have a winning advantage at all at the point marked in the notes?

Let's see. 42. Kf3 is indeed better - with the king on h3, black might have an idea with g5-g4+ and Rxh2+(#).
Next stop: 44. Rxc4. I think it isn't necessary to pick up this pawn; your central pawns become unstoppable after 44. e6! eg Rxe3 45. d5 and now e7 and d6 are next up. Rd3 can always be answered by Rd7.

The rest needs more than a glance to be sure, but the combination of Kh4 and c4 is clumsy at best. I think the last winning opportunity was on move 56: If you'd first played gxf4 and only then Kg4 the f-pawn is toast. Sample line: 56. gxf4 gxf4 57. Kg4 Re4!? (this seems critical) 58. Kf5! followed by e6+ Ke7 Rf7+ etc. I think in this line black's f-pawn actually hurts him as it means he can't check the white king from behind.

Yeah, 42. Kf3 is much better. h2 pawn for c4 pawn is a deal. Instead of 46. Rc8+ just keep your rook on c7 and patiently advance those pawns.

Too many pointless checks on his king. Only check when you can use it to gain mobility, or for some other tactical compensation.

And get the king in the center when the queens are off the board and the position is safe, like from about move 40 on.