Black could always move the rook to a1 before promoting the pawn. It forces a trade, but still leaves black with an advantage.

This is too slow. After 1... Bxf4 2. Ng2/Kh1/Kg1 Ra1, white can simply take the pawn for free with 3. Rxb2, and black loses all the advantage.

If white moves his knight to g2, check with the bishop at g3 also gets him another pawn and opens up the king’s defenses a little.

Trading a bishop for a pawn (one pawn that wasn't passed and only in the third rank) is not a very good deal, and black makes no progress towards promoting. Also, in endgames, king activity tends to be more important that king safety.