Another Long R+P Ending

FOLLOWED up yesterday's 64-move rook-and-pawn ending with one today that lasted 31 moves.
The main difference is that this time I was fighting for a draw rather than trying to win. The ending started in the following position:

White has just captured on d4 in Michael Bohnstorff (2044) - Spanton (1880), Bad Wiessee Senioren-Cup round four

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White is clearly better thanks to his superior pawn-structure. The question is: how much better? My main analysis engines, Komodo9 and Stockfish10, reckon White's advantage is worth about half a pawn.
22...f5
White was threatening 23.e4 as 23...dxe4?? loses instantly to 24.Rxd7.
23.h4 h5?!
The engines are not very keen on this. My idea was to prevent White from distracting my f pawn with g4, and to stop White gaining space on the kingside with h5. But it seems neither move is much of a threat, so the main effect of 23...h5?! is to weaken my kingside. Sensible was 23...Kf7.
24.Kg2 Kf7 25.Kf3 Kf6
The problem with 25...Ke6?! is that 26.Kf4 threatens 27.Kg5.
26.Rc6+ Rd6!?
This looks like a blunder, but 26...Ke5 is no bed of roses either as Black is very passive after 27.Rg6. The engines' mainline runs 27...Re8 28.Rf4 Rf7 29.Rg5 Rh8 30.e4! dxe4+ 31.Rxe4+ Kf6 32.Rc4.

Analysis position after 32.Rc4

Black has restored material equality, at least for the moment, but is clearly worse. One line given by the engines runs 32...Rd8 33.Rc6+ Ke5 34.Rcg6 Rd2 35.Rxg7 Rxg7 36.Rxg7 Rxb2 37.Rxa7 with a position similar, but inferior for Black, to one reached in the game after White's 30th move.
27.Rxd5 Rxc6 28.Rxd8 Rc2 29.Rd7 Rxb2 30.Rxa7 g6 31.a4 Ra2 32.Ra6 Kf7 33.e4
This seems to be the only way for White to make progress.
33...fxe4+ 34.Kxe4 Rxf2 35.Rxb6 Ra2 36.Ra6 Ra3 37.Kf4 Kg7 38.Ra7+ Kf6 39.Ra6+ Kf7 40.g4 hxg4 41.Kxg4

What would you play as Black?

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41...Ra1!?
The engines strongly dislike this, much preferring 41...Rc3 or 41...Rd3 (but not 41...Rb3?! as Black cannot check when White's king goes to g5). However, I am fairly sure the engines are wrong about the text.
42.Ra5
The engines give 42.a5 Rg1+ 43.Kf3 Rh1 44.Kg3 Rg1+ 45.Kh2 Ra1 46.Ra8, but this is not dangerous for Black, as they come to see after the continuation 46...Kf6 47.a6 Kf5. Black has three main tries here, but none works:
a) 48.a7 Kg4 49.Kg2 Ra3 (not 49...Kxh4?? 50.Rh8+) 50.Kf2 Rf3+ 51.Ke2 Rf7 52.Ke3 Rh7 etc.
b) 48.Kg3 Ra3+ 49.Kf2 Kg4 50.a7 Rf3+, transposing to the previous line.
c) 48.h5 Ra2+ (48...gxh5?? 49.a7 wins for White) 49.Kg3 Ra3+ 50.Kf2 Ra2+ 51.Ke3 Ra3+ 52.Kd4 Ra4+ 53.Kc5. Now it is safe for Black to take the pawn: 53...gxh5 54.a7 h4 55.Rf8+ Kg4 56.a8=Q Rxa8 57.Rxa8 h3 etc.
42...Rg1+ 43.Kf4 Rh1 44.Kg5 Rg1+ 45.Kh6 Rg4 46.h5 gxh5 47.Kxh1 Rg1
The remaining moves were:
48.Rc5 Ra1 49.a5 Ke7 50.Kg5 Kd6 51.Rf5 Rg1+ 52.Kf6 Ra1 53.Kf7 Kc7 ½–½