The first pass was assembled exclusively with Titebond glue, but in this next step, I went back and added a few exterior-grade wood screws to tighten everything up. I needed to make a strong column in the center of the base, so I cut that from a bunch of scraps, than stacked them up like a giant sandwich. More Titebond, then clamped for a few hours, we got that installed. Next, I cut a top from a piece of furniture-grade 3/4-inch birch plywood. I cut a couple holes, than mounted it on top of the tunnel supports, the 3" x 3" column, and a small support I cut for the opposite side. Now it's nice and sturdy across the center:
A few more wood screws and I think I could stand on this. That should be unnecessary, but at least if I should drop it, the interior structure shouldn't come apart.
I tend to be a stream-of-consciousness type builder, i.e. no planning other than a hazy idea in my head, and now came my first problem. The project required access for a power cord, but I hadn't thought too much about that. I had figured on just running it out through the access hole and out from under the base, but of course that would propped the base up slightly and was rather unsightly. The solution was to cut a small slot in the 1/4-inch base and cover it with a small piece of scrap plywood.
Another problem is that when I screwed everything together, the base warped slightly (maybe an 1/8-inch). It won't matter I don't think, but it's not perfect, for sure. We're moving on.