I don't think that playing with the shield connections of the FM cable will do the trick. I guess, that the FM pick-up coil is hit by interference. I would open the FM and try to shield the pick-up coil plus involved cabling.

You could also surround the whole FM by a soft iron plate, best bend to a closed cage. Or give unalloyed aluminium a try. Aluminium must not be bend as the iron plate, but must be extremely thick to work at low frequencies!

Of course, there's special shielding material available, but first test whether shielding will solve anything at all.

Kai