With all the pieces scotch taped in place, I started to apply plastic solvent glue on the inside and outside of all accessible seams. Once that had set I applied hot glue to as many seams as I could as well (just on the inside, obviously). Here are the photos of this stage:
Note that I have cut out along the etched line on the two side panels to make a removable side section. The removable section is actually made up of three panels.
The following day I started using expanding foam to make the whole structure stronger. Here's a view of the inside.
I need to wait for this to cure and then I should be able to turn the base upside down and add hot glue and expanding foam to the sections I couldn't get to yet. That is likely a job for next weekend.