Another Blown Rook-and-Pawn Ending

I MADE it 0/2 for my new club Battersea on Thursday, and the following day caught a train to Hull for the city's 54th annual chess congress.
My cold was still streaming, but I turned in a 178 performance against players graded 180-200.
It could have been even better had I taken my chance in round one ...

Position after White's 42nd move in Spanton (169) - John Cooper (199)

JC has been trying for 10 moves to win this ending in which his only advantage, apart from the massive grading difference, is the weakness of my g3 pawn.
Here he had to accept the inevitable draw that follows 42...Rxg3 43.Rxf6. Instead the game went:
42...Ke5? 43.f4+ Kd5
JC offered a draw. Much worse than the text would have been 43...gxf4+? 44.gxf4+ Kd5 45.Kf3.
44.Kf3 Rg1?
Another mistake. I expected 44...Rb2, with good drawing chances.
45.Rxf6 gxf4 46.gxf4 Rh1 47.Rf5+ Kd4 48.g5 hxg5 49.fxg5 Rg1
Here I rejected the winning 50.Ra5 because I could not see how the pawn would advance, but in fact the White king is perfectly able to see to that. Instead I played ...
50.Rf4+??
.... and the game was quickly drawn after:
50...Ke5 51.Rg4 Rf1+ 52.Ke3 Kf5 53.Rg2 Kg6.