No I haven't tried this. I'm only spit balling ideas.
Aerosol foam like Great Stuff brand is available in a variety of densities. I've seen it used on homemade coolers, bait tanks, etc... Low density should compress enough to pull the skin over it.
When you took your buckets apart, you found a substrate material, like burlap with wires in it. Without that substrate, the foam would slowly go through the springs like cheese through a slicer. That same material could be incorporated in the suggested rear seat plan but I don't think its needed. Foam fill from top to floor has nowhere to go.
I think I could fabricate a couple of metal tabs with screw holes to attach it to the floor pan.
