Jerry: I agree wax has more BTUs/pound (kJs/mole; troyouncemass-furlongs^2-fortnight^(-2); whatever) than cardboard.
Your egg-carton based solution is a wonderful low-price, disposable mini-cooker. Or a fire starter in really bad (wet, cold, frozen-wood) conditions. I'm going to try some out in my next round of experiments.
My practice of scavenging waxed cardboard produce boxes is better suited to fire starting only, not cooking. But, if cost or time were an over-riding factors, dumpster-diving trumps MYOGing.
Someday I'll try posting a zero-dollars gear list.

