It is relatively easy to remove the door panel to get a look at what is going on in there. Part of the removal requires disassembly of the door handle mechanism. You may find a bent part or orther offending piece of sheet metal. Then get creative in the repair. Maybe a strip of foam with adhesive backing where the contack occurs will stop the rattle. Let us know if you need help getting the panel off.
I loathe squeaks and rattles, too.