I hate myself

I hate myself when I lose game like this.

 That is not a legal move as white is in check.

But how about:

9. Qxg7 

20. Qd5 taking away counterplay. You are up a rook you don't need to worry abotu the a-pawn as much as your opponent attacking you with his queen. 

Loomis, isn't 9.Qxg7 met by Bf6? (Nxf6 Qxf6 Qxf6 Nxf6)

Seems too soon to initiate a queen trade

Kingfisher, in general it's a solid principle not to trade pieces unless it does something positive for you. But in this case 9. Qxg7 simply wins a pawn. White is well on his way to a winning endgame with the bishop pair and the queens traded.

But it also leaves white with a weak e pawn and the open g file for black's rook. It doesn't seem to get enough advantage to justify a queen trade.

In the line you gave, I don't see any weak e-pawn and I wouldn't worry about the g-file. A pawn is a significant advantage, I see no reason to pass on it because I want to keep more pieces on the board and wait for an even bigger mistake. I guess we can agree to disagree.

Incidentally, 9. Qxg7 Bf6 10. Bb5+! and now it really is all over.

9. Qxg7 Qxe4+ 10. Be3! is also winning for white.

I think 20 Qd5 would have saved your game.  You're already up a rook, why grab the pawn?  Simple greed is what caused the loss of this game.