Going down this path, even simpler would be to have supervisord starting a tmux session which starts the Julia app. Then one can simply attatch to the tmux session.
I just tried it and I can start a new byobu session to start a Genie app with:
byobu new-session -s "session_name" "bin/server"
This can be passed to supervisord
Update 1
Unfortunately, not so easy… By default supervisord would supervise tmux 
I think it can be set up so that the Julia app creates a pidfile and supervisor watches that. Will investigate, but it takes more digging…
Update 2
After more digging it’s a total no go. Looks like tmux can’t be started through supervisor.