I use a nested setup with screen where each level of nesting has a different escape key, this works really well when I want an inner screen to be on a different machine.
screen '-e^Zz' -S meta
and then inside that one screen '-e^Oo' -S project1
and for a session on a remote machine mosh some_server -- screen '-e^Oo' -S remote_session_name
I haven't figured out a way to get this to work well with tmux, because the local tmux server doesn't know about the remote tmux sessions. Whereas with screen, screen doesn't need to know or care about that.(edit: I use shell aliases, I don't type out the '-e^Oo' etc every time)