I was thinking through how you might do this, and my brain dredged up User-Mode Linux. A UML wrapper around those docker containers would behave almost exactly

I was thinking through how you might do this, and my brain dredged up User-Mode Linux. A UML wrapper around those docker containers would behave almost exactly like you describe. You should (if I remember correctly) be able to nest them, too. I'm pretty sure this is doable today. It's a monstrous hack, and I've got no idea what the performance overheads would look like, but as a way of hiding a mess behind a clean facade, I'm not aware of any reason it shouldn't work.