How to draw the endgame down a queen

Recently I played in the Chicago Open. I did not play many good games, so instead I will show one where I managed to escape with a draw after ruining my position. 

The following position is a theoretical draw:

As you can see, the defense hinges on stalemate in the final position. So if White had some extra pawns on d2 and h4 for example, then Black would be winning because the stalemate wouldn't work. But there is a way to add a pair of pawns that makes the fortress more robust:

In this position stalemate is not necessary to achieve a draw. This is because the a5 pawn guards b6. In the first example, b6 was the square the queen needed to go to in order to force the king to either abandon or block the c-pawn. And the a6-pawn shields the White king from checks if it is on the a-file and the queen happens to take on a5. So it does not matter if any extra White pawns are added to the board.

That was the idea I used to get a draw in my game. Turns out it was unsound because he could have stopped my king from getting to b7 on time, but maybe it was the best practical chance anyway.