With the script named "go", Here's what that allows in practice:
go foo.bar - Connects to host foo.bar
go foo.bar - Second connection to host foo.bar that uses same session, so keystrokes show in both, even if they originate from separate locations, like home and work.
go foo.bar 2 - Additional param is added to session name, so you get a new connection to foo.bar.
go -list - Lists all connection sessions, and only connection sessions, because there's a special prefix to distinguish them from normal tmux sessions that might exist on the VM.
go -restore - Spawn a new terminal for all open connections. Useful for getting all terminals back after the network drops, or you reboot, or you're on your home computer instead of work, etc.
Currently this is implemented in a batch script on windows with some ugly hacks to make it work well with what PuTTY's command line options support (commands for the remote host need to be in a file you specify...), and it's pretty ugly, but I'll share if if anyone is interested. It would be much easier in bash with openssh (it's even possible OpenSSH supports enough features to do this in the ssh config).