My shifter has recently starting moving, noticably, when I hit bumps lately. Any ideas on what might be causing this?

 

there is a place where the transmission is
attached through a rubber bushing (a cross
member) and then to the underside of the car
body. i would check this connection to see if
the bolt has loosened or if there is more play in
the bushing then should be there.

 

Or replace the worn out OEM shifter bushings with quality Poly bushings.
The "Hydro" engine mounts dont help any either.

 

A little play is normal when going over bumps, considering the squishy engine mounts and the urethane transmission mounts.

I have Prothane engine mounts, a K-member brace, torque limiters, and an MGW shifter... it doesn't move a millimeter now!