I finally got my cross-compiling SDK to Ubuntu 16.04 working. I was able to build the desktop app on my local Arch machine, scp it over to an Ubuntu 16.04 VM, and run it normally. The binary works perfectly on both the super old Ubuntu 16.04 and the latest Arch rolling release.
This is pretty exciting because it means it should be possible to ship a proprietary Linux app that will work naturally on most Linux computers, even though it uses GTK+3 and OpenGL for its UI.
I also joined IndieHackers today after years of lurking. I'm hoping this will help me stay focused on what needs to be done. I'm looking forward to posting another progress update, which means I need to actually make progress!