I decided to use basic butt joints throughout. The epoxy will be stronger than the wood itself, and when thickened it fills minor gaps nicely. In addition, I plan to add a few layers of fiberglass to the assembly when done, so the joints really don't need to be very strong. They just need to support the wood well enough to assemble and act as a mold.
So, I cut out the pieces I needed. I assumed a 4" box depth because it was a good compromise between avoiding cable strain and having a giant box clogging my view. I wetted out all of the relevant surfaces, then put together a mix of thickened epoxy to bond it. I clamped everything up very lightly in the center to remove a slight bow in the wood. Note that I glued up the 4" slats the night before using a box building jig. I'm building in sections to keep things simple.
Another design detail worth mentioning is my intent to have rounded corners. The problem is, with really thin plywood there isn't a lot of material in the corner to route out. My solution was to bond a 1/2" square block in the corner of all the joints. This will not only provide significant strength, but provide additional material to support the corners after rounding. The pieces are visible in the picture below:
After gluing up all the surfaces and letting the Epoxy dry completely I did some pressure testing on the box (nothing formal - I just pressed on it hard!) and was very happy with its strength. As a result I decided to forgo the fiberglass cloth. That saves a lot of time and hassle.
I used a round-over bit on my router table to ease all the corners, then gave it a hand sande down to 220 grit. At this point the box started to look really nice. To waterproof the box I gave the whole thing three coats of neat Epoxy. Now it looks not nice, but exquisite! Of course, it's not going to stay natural; I need to paint it white to blend in with the rest of the cockpit. But it almost looks good enough to keep as-is!
Next step is to remove the blush, scuff sand to prepare for painting, then give it as many coats as necessary of white paint. I chose Interlux Brightsides linear polyurethane paint. It was a bit tricky at first getting the right amount on and learning the roll and tip method. As a result, I would need to sand it down and repaint to make things perfect, but overall it looks fantastic. I'm pretty amazed.
Here is a picture of the finished product: