I would like to be able to ssh to a system and run a shell that will be persistent if my network goes down. The usual answer for this is to run screen or tmux, and then just reconnect to your disconnected session. Both of these programs basically run their own terminal emulator, so if you are running this in something like mate-terminal or xfce4-terminal, you can't use the normal scrolling methods to scroll backwards through your window. I am looking for something that would do something like their disconnected session code, but that does the minimum needed.
For example, I am envisioning something that where you would ssh into a system and start this program. It would run your shell behind a pty (which is how I think that screen does it) and would initially spit out something to identify the session name. If your network connection drops, you could just ssh back in, and run the program with an option to tell it to reconnect to that session. Basically, just like screen does but without all of the other stuff that comes along with it.
I've read about mosh, but if it runs across an encrypted channel like ssh for anything other then the initial connection I've missed that.