Why don't you put a seat belt on your bag? I usually secure all my luggage (of some weight) with seat belts when I drive, to avoid being hit by them in a collision. When driving to track events, even my helmet sits in the seat with the belt on.
I also leave the seat belts latched in the empty back seat to secure the seat back. If I carry something heavy in the trunk, the rear seat can fold in a collision, unless you have the seat belts on.