Close Shave

TURNED out for Hastings & St Leonards last night away to Maidstone in the Kent League (155 Average).
I had black on board two against a 163, with my seven-year Hastings & St Leonards unbeaten streak on the line.
It was quite a poorly played game, with both players missing winning shots.
Not for the first time, I was guilty of trying for too much in an equal position, and eventually we reached the following bishops-of-the-same-colour ending:

White to make his 53rd move in George Hollands (163) - Spanton (167)

White has a huge advantage. His king is more advanced, and two of Black's pawns are on the same-coloured squares as the bishops.
53.Bf7?
White must be close to winning after the simple 53.h4, which fixes Black's kingside pawn-structure, leaving him with two pawns on light squares and effectively unable to create a passed pawn.
I suspect GH missed my next move.
53...Bf3
I considered, but quickly dismissed 53...h4! But it was the better move, and is much preferred by my main analysis engines Komodo9 and Stockfish9.
The point is that after the practically forced 54.gxh4 (anything else allows instant equality with ...hxg3), Black is not in danger on the kingside and can hope to hold the queenside. However, White would still be much better.
54.Bb3?
Advancing the h pawn two squares was still the way to go. 54.Ke3 was also strong,
54...g5 55.a4?
GH offered a draw, which I gratefully accepted. White would still be much better after 55.h4, although now 55...f4 creates counter-chances. The engines give 56.gxf4 gxh4! 57.Ke3, when White is clearly on top but the game continues.
The draw means my seven-year unbeaten streak for Hastings & St Leonards has reached eight games.