Would the sled be sufficiently grounded if the back were mounted to the frame of the car using the strip of metal originally meant to mount the CD player?

Depends on that particular piece of car frame on your particular car. Some of the sub-frame pieces of the dashboard are not well grounded on some cars.

Grounding the sled should, in theory, be no different than properly attaching the harness ground wire. However, some have reported fixing ground loops by doing precisely that, so have a ball.