Is there any reason you aren’t using a two-container multisite installation then? I don’t think you lose much portability here, the quickest way to move instances between servers is by migrating a backup.
In the event you needed to move an instance you would just bring up a new server, mark the old instance as read-only, repoint DNS and restore the backup. With a low-TTL service such as Cloudflare handling DNS a small site can be migrated in minutes. Users would experience a brief period of read-only access, no content would be lost.
It’s much more efficient to divide up resources in this way, you won’t end up running two database servers and two webservers in separate containers and totally negates the need for the nginx reverse proxy.