I'm wondering if it might not be a good idea to have a hole on all (large sections) corresponding faces, for injecting expansion foam as you build, for strength and stability?
Unfortunately, expansion foam is extremely hard to control in this situation. My fear is that it would not only deform the pieces but may even cause them to become very hot as it hardens. I don't know if the heat would actually do anything to the piece itself but I don't think I'd chance it considering the scope of this project.
PVC is a good option as was done with the 8' ISS build. Or, use cardboard formers inside of the larger pieces. To be honest, Jan is SO good that I don't really think anything will be necessary to reinforce the structure IMO.
