Bishop endgame (Wright-Jiganchine, 1999)

10 years ago I lost an instructive endgame to a BC chess master Stephen Wright:



Black has a passed pawn on c5, so it may seem he is playing with an extra pawn, but that is just an illusion. He is in fact worse since his king is always tied down to the a6 pawn. I exchanged pawns on g4 which was a mistake, and since White got a passed pawn on the kingside, I quickly went down. For all these years since then I thought that by playing f7-f6 or f7-f5 I could have held this position. Now I realized that things are not so simple. Not to bore you with crazy analysis, please have a look at this possible position and tell me if my general reasoning is way off:



Black has to keep king on b7 or a7 to protect a6, and bishop on f7 to cover c4 and protect h5. When the Black king is on a7, White can play Bc4 and take over the diagonal (pawn endgame is bad for black). There is probably a way for White to break through this 'fortress'. f5 is an additional weakness that the black bishop can be forced to defend. I think White wins here