Hum... can't you just summon xinit from a TTY, and use ":1" instead of ":0"?
GDM might keep it's :0, but nothing should prevent you from running a different Xorg session, right?

Of course, here, I assume you're using Xorg, and not wayland. I have no idea if both can coexist and run aside on the same system, nor if ubuntu relies on wayland by default.