are there any really good ways to get out of the greek gift sac

no

...g6 or rook over fail immediately.

f advance (either) and white plays g6 and black can't escape or defend

Try f6. Not an ideal position, but it doesn't lose immediately.

 f6 loses to g6

Best thing to do is to read the chapter about them in Vukovic's The Art of Attack in Chess.