really weird but intriguing puzzle
White wins!

Wow, that was beautiful. I was thinking about after bd3, and qh4, we could play pawn to f4, blockading the queen from the bishop, so queen has to take, pawn takes, and white wins the game. Or am I missing something?

Wow, that was beautiful. I was thinking about after bd3, and qh4, we could play pawn to f4, blockading the queen from the bishop, so queen has to take, pawn takes, and white wins the game. Or am I missing something?
White almost wins but the moment White plays Pawn to f4 Black plays Qh1!, which defends the e4 square permanently.

Well than pawn takes e5, the f6 pawn is basically obligated to take, and now white has a passed pawn. The queen cannot defend both, and queen h6 check doesn't work, since white already pushed the f5 pawn to f6.
But your solution is obviously better, I've just noticed something, that's all.
After quite some break I have done another puzzle!
The puzzle shouldn't cause any problems to any experienced problem solvers, but it's quite sweet in my opinion.