Using CCF(Closed Cell Foam) pads for a frame is an old idea and a good one. You make a good point about two pads being needed to stiffen a frameless pack. The buttons you mention are really no heavier than using a bunch of duct tape to hold them together in use as a pad. The symmetrical loading of two stiffening members improves the ”tube style” of rolling inside.
The basic technique of using duct tape (DT) and CCF works quite well, at least till the tape dries out. This happens after about 4-5 years. DT sticks quite well to CCF. The entire pad, being fairly water proof and maintenance free, is not prone to punctures and leaks like inflatable or self-inflating pads.
The thickness of the pads can be a problem. With thin 1/8” or 1/4” pads, you can loose the overall effect of stiffening. Multiple layers of thin pads do not have the same stiffening effect as a single layer of a thicker 1/2" pad, nor the same warmth. Some textured pads provide pressure reliefs for lofting of a bag. Z-Rest, Nightlite, and some other pads provide additional warmth when used as a pad but sacrifice some stiffness when used as a frame. A Nightlite pad, for example, can interlock which adds some stiffness back when used with more than one layer, and, reduces volume from 3/4" for a single layer to about 1-1/8" for two layers...not the expected 1-1/2".
So, at last look at this method there were several variations that can be employed.
1) A simple rolled up tube.
2) A flat “fanfold” pad
3) A pair of smaller tubes as Eric describes.
4) A shaped stiffener pad
Of course, various combinations and reorganization of the basic shape you can cut and tape a CCF pad into. Longer pads mean more layers to a basic 20” pad. Often a 25” width is more dictated by the height of your pack, but is doable with most packs. All but the XUL or SUL packs being tall enough in most instances, even if it means extending into the collar, some.
Here is a basic diagram of the basic shapes: