You could add panel clips to the rear deck to help hold it down. If your real cheap, I've seen people stuff a wedge between the rear deck and the rear window to keep it from rattling all over the place.
Yes, there are 5.25 to 6.5 adapaters available. But... with the adapters, I'd be concerned about fitment issues, and everything clearing the door panel. It'* been a while since I've pulled doors in a mid 90'* Bonneville, but like every other GM, there'* not a ton of space to mess with, assuming that there are external brackets, and the don't bolt right up to the metal.
However, if they do bolt directly to the metal, a saw generally works pretty well to fit some 6.5'* there.