Adamis, agree, the movement is likely the result of multiple layers that are able move independently.
Building a frame is good idea I think. Can be lightweight either for removal or just payload.
I think the biggest advantage of building a frame is you can build it to fit tight in the truck bed. Then rubber mat on top of a thin plywood deck. If the deck to mat interface is still slipping, a series of “traction” screws in the plywood would secure the mat from slipping on the plywood.
Another idea is buy thicker foam. iDK the cost but I’ve used foam 2-4” thick sheets in construction. You can get 40,60,100 psi compressive strength. 40 is plenty. I was using in load bearing scenarios (lightweight void space under structural concrete)
FWIW I’ve never noticed excessive slipping with a bed mat directly on painted truck bed. It does move a little as I have a board that resides between the wheel well and camper. (Doubles as a short tailgate when camper is unloaded short term and the real tailgate is at home). I’ve noticed the camper has pinched that board tight on occassion.
So that could be another option. Take up the gap between the wheel wells and camper sides with a couple pieces of lumber slid in there with your current setup.
2016 Ram 2500, MotorOps.ca EFIlive tuned, 5” turbo back, 6" lift on 37s
2017 Heartland Torque T29 - Sold.
Couple of Arctic Fox TCs - Sold