I know someone did a test demo snap (http://bazaar.launchpad.net/~pat-mcgowan/+junk/testdemo/files) using webapp-container which uses oxide and ubuntu-app-platform. These aren’t actively being developed any more, but these technologies (and webbrowser-app from the Ubuntu archive (also not actively developed)) can use mir. I don’t know how appropriate any of this is for your project…
Also note Startx as a regular user