Nxc3 would be my move.  Now the king can escape to d5 for either of the queen's current mating moves.  Her own pawns prevent her from getting closer, so the rooks on the back rank can't even help her.

Disclaimer: it's been a long time since I've played chess, and I'm trying to get back into it, at least a little.  So I have plenty of rust to shake free. :)

Nxc3 is mate in two as t allows d5+ cxd5 (or Nxd5) Qf5#

Black's best bet looks like Ne3...

Wow, you're right.  Apparently I have a lot more rust than I thought. :)

I thought about Ne3 stoping the queen going to f5 or g4 for a turn however after qxe3 the threat of Qh3++ remained. I couldn't see anyway to prevent that.

Then I thought of Nf6 creating a place for the king to run behind.  White had two main options after Nf6.

1st. Qg4+ or f5+, kf7

or

2nd exf6+, kf7.  I think this was the better line for white

I couldn't see the correct followups, would nice if someone could say if it was on the right line or not.

Interesting game however.

 all other knight at d5 moves leads to mate.

 yeah Ne3 is the correct answer. Qxe3 with a new threat of Qh3#. but 2. ... Qxd5 pins the queen to the king.  with the queen off the board the mate threat also evaporates. 3. Qxd5 Bc5! again pinning the queen again recovering the given material. its true that black will give back all his extra material to survive but still he is worse here. with precise play white here should win.