Initially client knows only own hardware ID (which is just sha256 of part serials, MAC, etc.), and registers itself on server, which is allowed only from trusted networks. During registration client receives unique HTTP client certificate. Later administrator approves registration and assigns client specific stream. Stream may include sensitive information, like unique credentials to access some other services. Some overlays, which are not secret, like executables, 3rd party libraries, OSS stuff, are just rsynced to save time and bandwidth, but others like configuration and credentials, are downloaded over HTTP with client certificate authentication. Overlays are merged on client side in memory and applied in semi-atomic way (series of file moves within partition, not writes or other I/O in between).
There are a few other requirements, like log if devices tries to register second time, log if device tries to register from non-trusted network, log every update attempt, successful or failed, etc. And this is of course just brief overview. For instance, administrator approving registration is not a single person, but group of administrators, each with different permissions on streams. Client cannot download stream of some other client, and cannot get any information on overlays used by other clients, etc.
I do not see any way generic updater [framework] (not only TUF) to fulfill my requirements not causing more problem, than solved.