lets learn about defense here.
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. :)
Hm...it does look like 1... Ne3 buys Black a least a bit of time. If 2 Qxe3 Qxd4 3 Qxd4 Bc5 at least gets to the endgame; and if 2 Bxe3 Ke7 cold-bloodedly retreats to a safer square. Black may yet weather that storm.
Don't think that 1...Nf6 (ingenious though it is) quite works: 2 ef+ Kf7 3 fg+ Kxg7 4 Qe5+ Kg8 5 Rxf8+ Kxf8 6 Qxh8+ Kf7 7 Qxh7+ Kf8 8 Rf1+.
This has indeed been a very interesting position. At first (as per my original post) I'd thought it was just hopeless--but (as usual) the more you look, the more stuff you find.
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.