a tip I heard of from the dude from The Living End, who plays a Gretsch White Falcon...: He fills his guitar up with cotton wool, and then places black cardboard under the F holes so it still looks cool.

I dunno if this will loose that cool, hollobody sound, but may be worth a try, could be difficult tho, as you dont want to be stuck with little balls on cotton wool in your axe if you change your mind