There's nothing in the trays to vibrate, its definately the shifter hitting the chasis

Car mat ? is that it ? sounds too easy if ya ask me (I know you're not).
What about putting 2 layers of the rubber ? Or would that make things difficult ?
Does the rubber sit in between the 4 bolts on the shifter then is squished when the shifter is replaced ... making the gear stick slightly shorter than normal ?