Use a good quality piece of plywood. I personally like Birch. Cut to fit and apply several coats of Polycrit.
Go right over top the rubber mat. You'll want the extra insulation and noise deadening that the mat provides. Folks who have ridden in this van say it is the quietest one ever. Without the mat you will hear a lot of road noise and it sounds like you are riding inside a tin can!
The pallet will ride above the mat on the plywood. I never had any problems with the mat getting torn.
Moreover, the plywood is also there to create surface tension will the pallet to help it remain in place under hard or emergency braking...properly secured with ratchet straps and wood block locks in front of the load.
On my new truck, I used three rows of E-Trac on the floor. I really like that middle strap for those small skids. I cross the outside straps on small skids, but that middle strap gives me a much higher degree of confidence that the load is going to stay put when I have to brake hard in an emergency.
Leave the rubber mat on the floor.
As per Moot....use Stainless Steel fastners. I like carriage bolts, but it adds a lot of work. I just countersunk the plywood and used "Self-Drilling" fasteners. I have not had any problems with the screws heads snagging anything.