should the sled be isolated from the car's earth, or securely grounded?

It shouldn't need to be EITHER.

It should be at exactly the same ground potential as the rest of the player's casing and the player's ground wire.

The fact that you get noise when the sled is grounded and you lose noise when it's not indicates that there is SOMETHING WRONG with the wiring, either in the car, in the sled, or in the player itself. If things were working as they are supposed to be working, then it wouldn't make a difference whether you grounded the sled or isolated it or what.

I agree with Rob's diagnosis that it sounds like something is shorting out and actually applying a voltage to the frame of the dash itself. Do as Rob said, try measuring the DC voltage of the dash frame as referenced to ground on the battery's negative terminal. There should be zero electrons flowing between those two points. If you get anything other than zero, start looking for things that might cause that.