I stuck with it and managed to remove the player. This image is the front (driver's side.) You can see the two black plastic fasteners that hold the unit up after the bolts are loosened (they do not have to be removed.) These plastic fasteners are tough, and they held like iron.
Another look at the plastic fastener on the front passenger side.
To release the player I used this small pry bar (about 7 1/4".) It's a great idea to pry only between the metal mounting bracket, in the vehicle's roof, and the metal frame of the DVD player. If you try to pull down on the edges of the plastic trim panel, you might get lucky and pull the whole unit off, but you run a real risk of breaking off the trim panel's attachment points. At bottom middle (in the above image) is one of the four attachment points that are prone to breaking. The screw head has a red, green and blue paint mark around it. I found two of these points already broken (it might have been me; I tried this project once before in the spring.)