Took apart a swimming pool deck today. Wanted to save the wood. Lot of the screw heads rusted, striped out. Bought a 3/8" hole saw for my drill. With the pilot bit removed, I drilled a hole around the stripped screws. I was able to save the deck wood. It has a few holes but it's not busted up from prying.
I have a bit for my drill that deals with messed up screw heads wonderfully. It bites into them and backs them right out. I cannot really explain it, but you can find the bit at hardware stores, a little expensive but worth it.
I had situations where I needed the screws out without messing up the wood too.