I do something similar but instead of tmux in a terminal, I use a tiling window manager (called awesome) to achieve a similar user experience but with all GUI windows instead of only terminal windows. (it's not a daemon like tmux, though).
This way, I can also get a browser window in the mix too, or any other windowed application. I also prefer using gvim and not console vim, because I can have a different coding font and drag and drop files from my version control GUI (an enterprise VCS with a really crappy CLI, guess which one).
Switching to a tiling window manager is perhaps the best productivity booster I've had. It even allowed me to start working comfortably with one display only or a laptop display, I've always used multiple displays before.
I do exactly the same thing. It works really great for me. An additional plus if you go this route is the tagging feature of tiling window managers. This allows you to have multiple views. I use for example one e-mail/web view, one development view (vim in multiple consoles), one server view (consoles connected to various remote systems) one Matlab view and of course one music player view.
This way, I can also get a browser window in the mix too, or any other windowed application. I also prefer using gvim and not console vim, because I can have a different coding font and drag and drop files from my version control GUI (an enterprise VCS with a really crappy CLI, guess which one).
Switching to a tiling window manager is perhaps the best productivity booster I've had. It even allowed me to start working comfortably with one display only or a laptop display, I've always used multiple displays before.