I used hot-melt glue on the last “egg-crate” frame I made. I put it only in the right-angle intersections. It cools off slowly, giving you time to position the frame pieces and hold them at right angles until the glue is rigid. You can see how I did it
here. I should note that this is the ONLY place I use hot-melt glue. Gussets are, as noted, another good option.