I thought of this line, too. It just isn't enough.

Best, but Black's defences are just adequate.

Better was 35.Qxh7ch, but although White gets a lot of pawns, they aren't enough to match the rook.

It's Hope Chess since you're hoping for the best which is a mistake that would cost him the game. I don't think it'll be enough, but you don't know.

Cute!

I would play an intermediate check with 36.Rd1+. And, after he gets out, I'd then answer with 37.Kd7. Sure, it would cost black the Q for R, but it prevents checkmate since white is threatening 37.Qxc6#

Yes, and that's why I wouldn't have taken either. But, I can see where it would be easy to overlook, but I asked myself the question that Coach Stockel has asked me. Why did white away the Rook, and then came GM Susan Polgar's question. "What does my opponent want" Of course, that was his intention. I just don't know the best follow up, but with mate still threatened, I'd move the K.

I would've thought that this was mate. But, it appears to be the best move and what I'd now do, instead.

White had the initiative and the attack, but both were pretty edgy. Possibly White lost patience, or simply miscalculated into an unsound sacrificial line.

And, figuring that giving up a piece would do the trick which did not.

Thanks for all the comments.