Breakthrough puzzle queen and knight vs. queen and bishop with locked pawns.

In another thread that got closed I posted a solution like this to a fascinating endgame puzzle.  Computers don't help given their materialistic nature.  When I first saw it I didn't even calculate but 1.Nxb6??,axb6 2.h4,gxh4 and the queen when it reaches h1 is shut out so some calculation is obviously important too.  

The primary abilities you'll need however are schematic thinking and prophylaxis and eventually zugzwang and the principle of two weaknesses.  Did I get the solution right?  

I think I've seen that position before! Your solution seems to be correct, but I'm not completely sure if you've suggested the "best" moves for Black.

h4? and the bishop is locked out. I suggest 1 .. Qd8 and waiting with g5-g4 .. B/Q h4

yes, I don't see a way to play h7-h6, though this could be essential.

Why not at once Qd2, threatening with Nxc5 too.

I am not sure.

1.Qe2 makes the g4 break unviable:

1.Qe2,Qd8 2.Nb2,g4 3.fxg4,hxg4 4.Qxg4 and avoids harrassment from the bishop.

Probably not perfect but meh, the problem is about finding ideas not concrete analysis. 

yes, I don't see a draw, only different lines.

1.Qe2 Bh4 2.Nb2 nw if black cann't hold this weak pawn, sacrify it: 2 .. a4+ (too early? idk) 3.Kxa4 Qc7 ....