shifter

you might loosen the allen screw and screw the knob with button up or down a turn or three just to see if that makes a difference. This adjustment is present for how high the button rests, so I don't know if it would stop a rattle between button and knob.
To the bone... post reads like you car shakes much more than it should. Reminds me of what Harley riders call flumes. A Harley will shake aftermarket mirrors and such right off them. Those pieces fly past the heads of following riders like "flume".