How to win?

Ouch, guess I need to give up the visualization of this one if I want to get it right. :-). Perhaps just 37. Qc3 trying for a draw.

37. Qc3 doesn't seem like the best option due to the exposed white king. I think she needs to get back to defending.
37. Qc3 is met with 37. ... Qg3
This is how it looks now:
If white takes the e-pawn, the black rook will take position on the 2nd row with another mate threat.

I saw 39. Qg1 but missed Qg8+ After further analysis, white looks better here.
So 37. ... Qg3 is the better choice for black.
Back to the original question. 30. ... Qxe3 for the draw, otherwise b6 would be the better choice to attempt a win.
This was fun!

