I'm still struggling to understand what advantage Docker brings to the set-up.
Maybe the application doesn't need to write anything to disk at all (which seems unlikely) but if so, then you're not saving any disk-write cycles by using docker.
Or maybe you want it only to write to filesystems mounted from longer-life storage e.g. magnetic disk and mark the SD card filesystems as --read-only. In which case you could mount those filesystems directly in the host OS (indeed you have to do this to make them visible to docker) and configure the app to use those directly, no need for docker.
Docker has many great features, but at the end of the day it's just software - it can't magic away some of the foundational limitiations of system architecture.
That all seems ... incredibly complicated.
Why not use fwupd? (link is the Arch wiki but should be relevant for any distro). I've been using fwupd to keep my Dell XPS15 BIOS updated for the last few years, with no problems at all.