The only energy I want to dissipate is the egg's energy, which is independant of the shell, no? And my diagram is very imperfect, imagine a perfect circle. The purpose of a sphere of superballs is to maximize the force of gravity on the entire structure as a whole, rather than on a component of say, a rectangular prism, as well as to have a round surface contacting the ground on every collision, no matter what the orientation.
I don't understand how radial springs would be used, I'm not familiar with this type of spring. Also, what do you mean by supporting sphere? The sphere I'm using as a template to make the bouncy ball shell? I intend to use just a foam ball I bought, glue together half the bouncy balls to be used, and then do the other half without gluing the two halfs. I'll have to find a method to attach them for trials, I may do an entire half, fashion the springs to the interior, then do the next half without gluing the top "cap" (think kippah (jewish headwear)), so when I'm done fashioning the springs to THAT half, I can glue the two halves, and have a removable cap.