Dv hooked me on using Tmuxinator with iTerm 2 as a way of getting my rampant terminal usage under control and while it still makes me swear like a sailor from time to time, I found that if you add this to your ~/.tmux.conf file:

set-window-option -g allow-rename off

That tells Tmux to NOT allow the process that launches after the window is created to rename the window. Thanks to jlipps for asking the question. Oddly enough, jlipps wrote the original version of AppData which I rewrote and now own with Jared. Small damn world.