Hi, Amana. The 24 or 36 grit sandpaper will make short work of the poly and about anything else, too. Remember that you will be removing about 1/8" of wood and that is a lot of dust. Keep a watch for nail heads as they will tear up the sandpaper. And use plastic sheeting and masking tape to seal up door openings. Don't forget to seal heat ducts or other openings also. Wear your dust mask and hearing protection.
After you have gotten dust everywhere, you need to go back to a dust-free environment for the finishing. This will give your shop vac a real workout. And don't forget to tack rag all the wood.