I wrote https://github.com/zdykstra/tmuxc as an alternative implementation of iTerm2's tmux integration. It's terminal agnostic; it just runs a command for each terminal. Depending on the terminal you use, you could probably make it spawn each tmux pane into a dedicated tab.

It's very much designed and built for my specific needs on my specific desktop environments, so there's no promises that it'll work for you well ... or at all.