I still think Kg7 is only option. Maybe not h5 right away after g4, but first Re8. The white position has a weak spot with g4. We better exchange queens if our queen is only defending a pawn, and the white queen has many attacking threats. Also Re8 right away is better than Rc8. That Qf8 variant I overlooked, but saying I have no clue makes no sense.
Just trying to make suggestions, so together we find the best move. That's why I asked if I only give my move, or also give suggestions. I hope you all look at all the possibilities Kg7 gives, that was my only intention. Kg7 to me looks like our only chance.
Best case Kg7 will transpose the the line I already gave. Worst case our king will be on a slightly inferior square in the endgame. For that reason Re8 before Kg7 seems slightly more accurate and flexible as it gives us the choice below which would otherwise be missing.
I still think Kg7 is only option. Maybe not h5 right away after g4, but first Re8.
30.Qxe5 Qg6
31.Rc6 Kg7
32.g4 Re8
33.Qxe8+ Nxe8
34.Rxg6+ hxg6 (34.Rxg6+ Kxg6 would not be an improvement for us because after 35.Bc4 our king would be misplaced on the b1-h7 diagonal allowing white to gain more time. 34.Rxg6+ fxg6 looks bad because of 35.Bc4 a5 36.Bxd3 h5 37.Be2 hxg4 38.fxg4 Nf6 39.Nc4)
The line above transposes to my original line except that we now have a choice of where to move our king on move 34:
30.Qxe5 Qg6
31.Rc6 Re8
32.Qxe8+ Nxe8
33.Rxg6+ hxg6
34.g4 (
we now have a choice of Kg7 or Kf8 breaking the pin on our f pawn. I think Kf8 is better as a slightly faster way of centralizing our king)
Upon further inspection I have decided that this endgame (after Re8) will be a harder to draw than I originally thought (but still very possible). I have decided to vote for Rc8 instead and keep the queens on the board. The queen endgame will not be simple either so this vote is primarily a matter of taste.
Rc8: 5 votes (galdur, boolberry, ING Bank, XMRpromotions, languagehasmeaning)
Kg7: 1 vote (Rolf Uhlhorn)
Re8: 1 vote (LucyLovesCrypto)