A good lesson indeed. Interesting game. (I agree 39.Qg3 looks better)

the 34 Rxf6 blunder was not so much of a stab, but i really felt the 39. g3 in my soul after thinking about that move for so long :P  . 39.Qg3 seems to be a win, but i missed at the moment of playing that it would still cover g5 forcing a trade else 40.Rh7#

I guess its a lesson to never give up when you are behind