When I compared the pressure box to the lid, I discovered that while the lid was almost perfectly square, the main part of the box was slightly out of square. It also rocked slightly when I set it on a flat table. In order to square up the box, I decided that some mechanical fasteners were in order - I didn't want to rely on just gluing & clamping.
So, I put the lid in place and using some hardwood scraps, I clamped the lid and the box together, side to side and end to end, to forcibly square the side/end assembly (with the already square lid):
Then I flipped the arrangement upside-down, and drilled some pilot holes for some small screws so that they would screw into the centerlines of the hardwood reinforcing strips that were glued to the lower edges of the side and end pieces:
Before gluing, I drove all the screws in to the bottom panel so that the points stuck out slightly and would "find" their pilot holes in the side/end assembly:
I then applied glue to all of the bottom-facing edges of the side/end assembly, set the bottom panel in place and tightened down all the screws:
Once the glue had dried overnight, I found that everything was square and flat, and I got a nice square fit with the box and the lid.
