I did something (slightly) similar via proot, called Bag [1], which I must have not described as a docker alternative: It has nothing to do with cgroups, and the cli deviates from that of docker's.
The backstory: To bypass internet censorship and deep packet inspection, I had written a proxy chain solution masquerading itself as plain html traffic. I needed it constantly running everywhere I went, but I didn't want to port it to a native android app. I wanted to run it through termux and at the time termux had no jdk/jre. Proot could spawn a archlinux env and there indeed was a jdk available.
The arch env within termux turned out to be generally more suitable for all tasks. Creating and destroying ephemeral envs with different setups and prooting into them to just run a single command is easily automated with a script; I named it bag.sh, a drastically smaller form of a shipping container.
Funny bag.sh also has a roadmap/todo in there untouched for 5 years! It's written on mobile screen hence mostly formatted to 40 columns lines to fit on the display without scrolling.
I guess a lot of us had stories like this. I needed to package a bunch of things into a single environment where a VM was unsuitable. I cooked up something using chroot, deb-bootstrap and make an installer using makeself. It created a mini debian inside /opt which held the software and all the dependencies I needed (mysql etc.). Worked pretty well and the company I made this for used it till they got acquired in 2016 or so.
More generally though, implementing a crude version of a larger application is one of the best ways of learning how things work inside it. I'm a big fan of the approach.
Now I'm kinda tempted to have a go at this using distroless, probably by building a container using the already existing tools and then slurping the contents back out of it to turn into a chroot.
I managed to coax my 8" tablet turned horizontal to give me about 80x22 at a size I could actually read.
Combine that with a ~10" bluetooth keyboard that fits comfortably in my leather jacket's inside pockets and I get to leave the house without carrying a bag and still sit and write code in the back corner of a handy beer garden.
Turns out to be surprisingly productive as well, probably because there's just enough extra friction to flipping to my usual distractions compared to a laptop that I tend to just take a sip of my beer while continuing to glare at the code instead.
True! A tablet and an ext-keyboard do a much better job (Although I wrote bag.sh out of boredom while stuck in a beer-less airport waiting for a delayed flight; I hope I won't have to actively plan for this setup again)
I have a stack of Thinkpad Tablet 2 bluetooth keyboards (though it's getting a bit low, will have to find somebody on ebay or whatever that still has some again soonish) - they're capable of being paired to more than one device (I also use them with the tablet half of my Helix 2) and have a built-in stand which takes my 8" tablet just as well as it did the Tablet 2 itself back when I was using that.
So had I ended up in the same situation as you I would probably have done similar, but with an added undercurrent of "Matt, you idiot, how did you manage to forget to put the keyboard in your pocket before you left?!"
(still a neat hack on your part, mind, no question there, but I'm very much glad I've optimised by standard "leaving the house" loadout so inflicting the same thing on myself is at least *less* likely ;)