An Ending Not Fully Played Out

MY round-six game at Alicante - the full moves can be seen here: https://beauchess.blogspot.com/2021/12/alicante-round-six.html - reached the following position after 48.Rd2-d7:

How would you assess this rook-and-pawn ending?

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Material is level but White has a protected passed pawn, albeit one that, for the moment at least, is blockaded by the black king. Both players' queensides are vulnerable to rook depredations.

After 48...Rf1+ 49.Kg3 Rg1+ 50.Kf3 Rf1+ 51.Kg3 Rg1+ I played 52.Kf3 and offered a draw, which was accepted.

I felt that after 52...Rf1+ it would be too risky to play 53.Kg2 as Black more-or-less cleans up on the queenside, starting with 53...Rb1.

But the analysis engines Stockfish14.1 and Komodo12.1.1 reckon White wins with 54.Rxc7 (54.Rh7 also seems very strong) Rxb2 55.Rh7 Rxc2+ 56.Kg3, reaching a position in which Black has many plausible continuations.

Position after 56.Kg3

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A) 56...Rc3+ 57.Kh4 (57.Kf4? is dead-equal, according to the engines) Rxc3 58.Rxh6+ Ke5 59.Rxb6 c4 60.f6 wins for White. Black could try 58...Kg7 or 58...Kf7, but 59.Rxb6 still wins.

B) 56...Kg5 temporarily protects the h pawn, but 57.Rg7+ Kf6 58.Rg6+ Ke5 59.Rxh6, or 58...Kf7 59.Rxh6, wins for White.

C) 56...c4 57.Rxh6+ Kf7 58.Rxb6 Rc3+ 59.Kf4 Rxa3 60.g5 wins.

D) 56...h5!? may be Black's best try. But after 57.Rxh5 Ke5 58.Rh6 Rc1 (this is best, according to the engines) 59.Rxb6 c4 60.Re6+ Kd5 61.f6 Rf1 62.g5 c3 63.Rc6 Kd3 64.Kg4 c2 65.Kh5 White seems to be winning, eg 65...c1=Q 66.Rxc1 Rxc1 67.f7 Rf1 68.Kg6 etc.

CONCLUSION: Playing on after 52.Kf3 was much less risky than I realised; indeed the engines convincingly show White is winning.