I don't understand what docker problem would be solved by multiple git directories but not by multiple work trees?

Regardless of whether the former solves it, I was going to suggest you could use compose or whatever in your 'human' tree, and then tell the AI to use equivalent docker commands without using compose, so it gets anonymous/its own named containers, but you keep the convenience.

I use Conductor's spotlight (and a Pi extension I derived from it) but it's not perfect. Once a migration executes, I'm pretty much bound to it but at least once, I have just backed up the database before switching and then restored that.