Finally got Chromium browser running as an xdg-app, and not just building (which was nice too, but not that useful), as a result of my attendance to the GNOME Software hackfest. And it even seems to work!
Anyway, this is far from over, but for now I'm quite satisfied with the results. Special thanks to +Richard Hughes
for inviting me over and to +Alexander Larsson
for his help with my dumb questions during the hackfest!