Hxg3 would lead to white's two rooks vs Queen, which is probably still a win, but I like Qh3. I think it says it all. It will win the rook on g3 and with white's control of the g file and doubled rooks, along with black's exposed king, mate isn't far behind. I just glanced at it though so I could be wrong. Interesting puzzle with all the pins.
Maybe force the black king to the h file and then play pawn takes rook, which will take away the chance of black immediately pinning the white queen and king?
RxG3 RG7 QxG7