How can I reglue sheeting that’s lifted on core, or can I steam it back down? With weight
Not sure this will be any help but back in my sailplane days we used a rubber based contact "glue", I think it was from 3M. It rarely came lose but you could cut a thin slit in the skin (we used super thin hardwood vanier) with the grain and shoot in some fresh adhesive if simply heating it with a monokote iron didn't work. I am sure things have changed. Don't much like the steam.
I have used farm store hypodermic needles to inject CA into a crack. Why couldn't you use one to inject some foam friendly glue?
Ken