I'd second the notion of building a fixture to attach the boxes.
3/8 or heavier partical board or plywood; cut to the diameter of the bottom of the egg, and use some small strips of wood on the inside to glue/screw/secure the box-sides. Then, you can insert the wood into the shell, then probably glue and staple, as long as the egg plastic is soft enough to not split from stapling... Or just drill some minor pilot-roles before stapling.
Using a wood base will also give you a solid foundation for mounting landing gear and engines later.
When alighning the 'bays' to the hull, it may leave some gaps; just fill those with epoxy and shape it after it dries. Once it's painted, you won't be able to tell.