I do the above as well with 1 addition, any of the virtual tabs on my remote host can also run a screen themselves. To control this I use Ctrl-Oo to control the outer screen and ctrl-a for inner screens. This is useful when you have a remote dev server for a particular app and want need multiple connections to it, such as running nodejs server and tailling the output in one shell while using the editor in the other. I only started using this recently but it has worked very well.
In my case, I tend to ssh to one remote host, where I have a tmux session running with its own tabs, each of which is ssh'd to a bunch of other machines (10+).
By doing it this way, I can access all my remote ssh sessions from anywhere by just accessing that one initial machine and connecting to the tmux session.
I currently use tmuxinator to recreate the whole elaborate construction if I ever need to.