I don't think foam is a good idea. The problem is that if you compress foam to 25%, the cells can still expand and bulge, and the whole point of compression is to prevent that.
Consider, the 11psi figure is given at a specific state of charge. As the cell charges and attempts to expand, that figure will naturally go up, as the compression frame should not have any give within it. And at full discharge, the figure should go down. The mechanisms that lead to expansion I don't think are that simple, but that is the general idea.
It (IMHO) isn't the 11psi that is important. What is important is that you apply enough pressure to stabilize the aluminum case, so that the case cannot distort as internal pressure in the case rises. But not to apply too much initial pressure to distort the case.
Efforts to maintain exactly 11psi, with foam, springs, or whatever, defeat the whole purpose of compression, as they allow the cases to distort as internal pressure rises.
I feel that it is most effective to simply tighten the frame so the cells are firm to each other.