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.