King and Queen Vs. King and Bishop's Pawn

OK, I'm working through Queen and Pawn endgames, and I've figured out how to win the following position:

Basically, the key is the position of White's King.  When the White Queen works the king to b1, white's king can take two tempi to move into a checkmating position.  Black will Queen but it doesn't matter.

Now, according to Yasser Seirawan, the same thing works for a pawn on the c- or f-file, only more so.  The White King's "zone", in which the game is objectively drawn, is acutally larger.  The problem, I can't figure out how to win:

It seems like Black can draw here.  What am I missing?

Well basically the idea when playing

"King and Queen vs King and Rook/Bishop Pawn in 7th" resumes on 1 simple idea

is the strong king able to make it to the critical squares? if yes then its a win other case its a draw.

Here you may ask wich are these critical squares? Actually its really easy to remember.

1st. for rook pawn on 7th these squares can be found imagin you have a knight on the queening square the critical squares are the legal moves for that knight if the strong king can make it to any of these squares within 2 moves then he's in the critical squares

2nd. for bishop pawn on 7th depend on the position of the weak king it can be on the week side (1st diagram) or the strong side (2nd diagram)

if the weak king its on the weak side the critical squares for the strong king are 

once again if the strong king can get in any of these within 2 moves its a win

the critical squares for the strong side of the weak king are 

here the strong king must be able to be in any of these squares in 1 move other way its a draw.

In a roughly explanation thats it, hope this can solve your question.

The black king is on the weak side, which means that he can't easily use the stalemate defence by moving to a1.

 Here's my variant. Did I make any mistakes?