That's the kind of input I was looking for! I think canvas should work perfectly for this, but you don't need adhesive. The wires will hold it in place.
I actually completed this project yesterday when the weather was nice. Looking around at what I had on hand after I started this thread, I found a heavy duty shopping bag that's very similar to canvas that should work. If I had used that, I would have put a piece of a thin yoga mat in the bag. Probably wouldn't need the mat, but it seemed like a good idea. But then I found a thin rubber floor mat with carpet on one side. The seats in both my Sport Tracs are some I swapped in from 1998-99 Explorers with the manual lumbar adjustment. Since the driver's seat in both trucks are identical, I pulled the driver's seat out of the '01 that's not running and inserted a cut-to-fit piece of the floor mat between the foam and wires with the carpet side toward the wires. I didn't test it, but it looked like it'll work, so I did same with the seat in my '02 yesterday.
In both seats, I found 1 broken wire, and 1 spring had come off, in addition to the wires cutting deep into the foam. I knew the spring had come off 1 seat because I felt it go. Not much way to fix the wires, but putting the spring back on was easy enough. You don't need to remove the foam from the seat for this fix. Just peel the upholstery back and tilt the foam to get access to the bottom of the foam. After driving 75 miles or so last night and today with the spring and floor mat in place, I think this fix was a success. Before, it felt like my butt was almost on the floor, but now the ride height is what it should be, and the seat is firm without being too harsh. Whatever you use, keep it thin. The floor mat I used is as thick as you'd want. Canvas should be fine.
A couple of things I learned -
Removing the foam from 2nd Gen Explorer power seats with the adjustable lumbar is more complicated than pulling the foam from a manual seat with no lumbar adjustment. The adjuster cable runs through the bottom foam at the rear inside corner, and the wiring harness for the switches runs through the upholstery. The adjustment knob prevents the plastic trim with the switches from coming off the seat. There's surely a way to remove the knob, but it isn't necessary for this project.
I removed the 1st seat I did from the truck and then took it apart. I tried to take the 2nd seat off the track in the truck, thinking that might be simpler and quicker. It's possible, but wasn't quicker or easier. I ended up unbolting the seat track from the floor, but didn't take it out of the truck. Removing the seat and track as a unit and taking it apart outside the truck is the way to go.