It looks like the lip pieces are attached to the edge of the top, i.e., that the top is the same size as the rest of the case.

If, instead, the top was the size of the case plus the lip, so that the lip pieces were sitting on the lid while the case was upside-down, the force would be much better distributed and you would need even less hot glue because the lip pieces would be fully supported.

Of course, I could be wrong about that observation, in which case you're ahead of me.