An update on this project is long overdue, but the good news is that there's not really a lot left to do! Everything is wired up and running fine on the hardware side of things, with the only two chores left to figure out are getting the capacitive touch feature of the screen to work, and to cut some holes in the case I've chosen to accommodate the screen and the various switches and ports required. On the software side of things, I decided to ditch Lubuntu in favor of Arch Linux, partly because I wanted to run XFCE, and also because I like the idea of a more ground up approach to my operating system.
I'm honestly at a bit of a loss as to how to get the touch input working on the screen. It plugs in via USB, and when I run lsusb in the terminal, it recognizes it as being plugged in, but it doesn't recognize any touches. It shows up as an NTrig screen according to lsusb; I'm still exploring options as to how to get it to work. I don't know if I need to update the firmware on the screen (not something I've been able to find for that particular board on the manufacturer's website) or if I just need to recompile the kernel with altered options. When I plug the screen into my x86 devices (a Mac Pro and a laptop running Ubuntu) they both immediately work, so those are the only two options that I know of to try.
As for the enclosure, that's just a matter of buying a router or a dremel with a blade, which I haven't done yet.