People often glue plastics, when they are better fused with heat. plastics generally can only glue to their same kind of plastic. you can glue a hole in a tub which absolutely no glue adheres to by melting a piece of itself to itself. ideally though the temperature has to be very controlled and not flame temperature, so if you can get it liquid in a non food oven that's good.

gluing foam is very difficult because it changes shape so fast when it heats. Although... there may be some obscure ways that work, that you can invent...

For example, if you put a layer of salt water on top of one foam layer, and then put another foam layer on it, and then put 6000 volts through it very briefly, perhaps you can make a controlled melt lightning.

please tell us how you get along.