Ultimately, I gave up and created a separate Ubuntu VM to run as an NFS server. Every CoreOS instance mounts it, and then my data-only containers now map back to the NFS mount. This way, when CoreOS moves the Redis or PostgreSQL containers, it has the data available to it.
It's not my favourite setup, but it's worked well-enough this past week that I haven't had to manually correct things while on vacation.
I'm hopeful that someone smarter/more experienced can share a better solution.