>every byte has to be parsed twice, once by the middleman and once by the terminal.

The ~ (tilde) codes in OpenSSH imply that it also performs minimal parsing. Particularly, "(return)~." to terminate a locked session.

The tmux program is invaluable to me when I have a long-running set of interactive commands, and I want them to survive a network disconnect.

There may be valid criticisms of tmux, but wow is it good at this particular thing.