I wouldn't move it if it were me. I'd rather come up with a different way to listen to music, like a hidden bluetooth receiver, than drill a large hole in a spot where it doesn't belong on one of these cars.
First try grounding the antenna. Run some temporary alligator clip leads from the antenna ground to various grounds on the body and see if your radio stations come in better. If they do, then you know you can just add a permanent ground wire as a work around for the fiberglass issue.
