Since your pump is below the pool you have additional pressure because of the location. The lids are designed to seal better under a partial vacuum and not positive pressure. My limited experience with a twist off lid was.....junk it. usually difficult to open and close compared to the one you have. For a suggestion how about a really large hose clamp around the middle of the lid and the basket body to help even out the hold down force? The hold down screws are at one end and tangs at the other. The hose clamp would give some middle force. Might also put some strips of rubber such as from an old inner tube between the hose clamp and the lid to provide a little cushion and help even out the stress from the clamp.
Al