Did you get your answer to this?
A couple ideas: you could build the image and push it to a private registry that may be accessible to the private network? That way you can just pull from there.
Or you could think about using something like KOTS (but I've only recently started looking at it, so new to me too).
Or you can save a docker image as a tarball, move it to your private network, then load it back in.
Hope you got your solve though. Sorry I didn't reply sooner.