Originally posted by Fat Lady
E.g. 40. ... Qe4+; 41. Kg1 Rxg8 42. Rxa2 (not 42.Qe8+ Rg8; 43.Qh5+ Qh7)
In your line Rxc6 instead of Rxa2 and white threatens Rh6+.
I checked the 40…Qe4+ lines with Fritz8 and Black cannot do better than a draw by perpetual. Black’s first priority is to cover g7 and can do so two ways: by Rxg8 or Qxe5. If Black plays the latter white has Re2-e7 or Re2-f2-f4 resources depending on the line and has at least a perpetual in all lines.
So 40…Qxe5 warrants consideration and I have not yet find definitive winning lines for Black after Rxc6 Bb1 Bxg7+ Qxg7 Qxg7 Kxg7 Bxd5 Ra6 Rc1. I think this line is best and white's moves forced.
Black to move.
Playing through the lines, this looks like a draw.
I expect there are improvements to be found earlier in the game.