It turns out Keegan McAllister (kmcallister on github) ported Mosh to
Android a few weeks ago, but ran into an issue with the pty not having
rows and columns set in their shell (I think it was through adb). I
figured out that this doesn't affect Terminal Emulator or Better
Terminal Emulator Pro, and it can be worked around using stty anyway.
I also wrote a shell script for the ssh wrapper that starts the Mosh
server (mosh-server) process on the remote host and gathers the port
and encryption key to pass to mosh-client. The default wrapper is
written in Perl and relies on IO::Pty which is apparently kind of
tricky to get onto Android. My wrapper works on non-rooted phones
with kbox installed, or on ROMs like CyanogenMod that already have
busybox and OpenSSH installed.
Details here:
https://github.com/keithw/mosh/issues/32
Next step might be to do a fork of ConnectBot, if possible, that
starts a pty and runs the wrapper. If that's not feasible, then a
different GUI from scratch might be needed, but that seems like
unnecessary duplication of effort if Mosh can be integrated into
ConnectBot.