Just a point of note, I boot Fatdog, loading it into ram, and then run a container that is pretty much my daily system within Xephyr, unshare, capabilities dropped, chroot using the main sfs that's already in ram as its image. Very similar to (and derived from Barry's excellent work) EasyOS.
Instead of booting the main system (DISPLAY=:0) and then starting the container session (DISPLAY=:2 (whatever)) I just boot Fatdog to cli (pfix=nox) and then run
X :2 &
DISPLAY=:2 container.sh
that starts a X, and then with the container initiating the Xephyr ...etc.
No main gui Fatdog session, just a cli. The only X is the containers :2 display. I find that runs much faster/smoother (and fonts look nicer) than if there is X running on both :0 (main session) and :2 (container).
When you first run X :2 & the display flips over to graphical ctrl-alt-F4 (or whatever, according to the configuration of number of consoles) display (black screen) and you have to ctrl-alt-F1 to switch back to the (text/cli) console session to run the DISPLAY=:2 container.sh script.
It's also nicer in the respect that there's no host grab focus toggle issues, it consistently remains locked into the container session. And I guess no conflicts between main session configuration of display ...etc. and that of the containers configuration.
IIRC Xephyr is a framebuffer type overlay on top of the main X, so simpler/faster, and for me at least a very noticeable difference when that is the only X instance running. I don't mind having Fatdog main session as cli based as I don't access that much. I just boot, use, shutdown without saving once I have the system configured as I like. When I do make changes I remove the pfix=nox boot switch and boot the full Fatdog main session/desktop which I can use to make the changes and rebuild the main sfs before returning to booting pfix=nox again. For 'remastering' I just have the main sfs extracted out (unsquashfs) and after any saves (multisession....save files) are just added to that (squashfs-root folder, using unsquashfs -f -d squashfs-root multi....sfs) and then the new fd64.sfs created from that (mksquashfs squashfs-root fd64.sfs -comp lz4).
I've lost track of EasyOS, I think it was a 2.x version I last tried. So don't know if any of the above might be of use/help, but posted just in case it might. I don't have as much free time these days what with being the sole carer of a 90 year old (mum with dementia).