I've created a prototype of a "compartment cover" for this last trip I went on. I have some adjustments before I finalize it and have a real one made.

It will cover the entire back section including half way up the sides. The front section of the cover slips over the "stored" (Flipped up) rear seat to protect it from dancing claws and performs a barrier between the the front of the rear seat and the back of the front seats to keep them from rubbing and making noise. (If your front seats go back that far).

I'm looking to have the floor section to be made of the same type of material as above then have quilted material for the pad part. The intent is to have the pad removable from the floor part for washing purposes.. I'll post again when it comes closer to fruition and either will provide the whole thing available as a bought item, or the plans/pattern so your local upholstery shop can fab it up.