As a certified "Old Timer" (Boy Scout in the 50s Happy Daze) I remember the frameless Jensen packs. They required two vertical compartments to be stuffed full for the pack to attain proper rigidity. (The hipbelt was also made to be stuffed!)
I think a similar principle can be used with a sleeping pad today,but using a closed cell foam sleeping pad in a different way than is curently done.
1. Cut the CCF pad horizontally at the mid-point. It can be re-joined using wide Velcro glued on both sides in a -_ fashion. (one narrower 1" female strip glued entirely on the pad, one wider 2" male strip hanging out and just glued on half of its width.)
Glued on snap straps could also be used with the glued part of the strap wider for more surface area to hold better.
2.Turn a current commercial or DIY frameless pack inside out. Sew two vertical columns into the inside back. i.e one piece of hemmed fabric stitched vertically on each side and then down the middle, leaving enough room in the two columns to JUST fit the tightly rolled halves of the sleeping pad into each column.
This should give a lot more rigidity than current folded foam pads do, leaving almost as much room in the pack.
Not enough room inside the pack? Try adding a heavy mesh dual column on the outside back. Unlike the internal columns it will have to have the bottom closed and the top sealed with a male/female strap of a 1" Velcro strap passing thru a tethered plastic ladder slider at the top of each column and back onto itself.
Obviously the external method will require re-asjusting the pack straps and belt.