More suggestions Rated 5 out of 5 stars

Another vote for: Click on the group in the menu to select the last selected tab in that group.

Also, another interesting idea:
Have an option to make each group its own dropdown menu. The title of the menu would be the group's name (or possibly an icon, selected from a preset list).
For example:
[Social sites v] [Music v] [Games v]
These menus could live on the right side of the tab bar, to the left of the groups area.

This feature would be optional - the current solution is also good. This would allow you to select tabs with 2 clicks instead of 3.

This review is for a previous version of the add-on (0.4.1-signed).  This user has a previous review of this add-on.

"Click on the group in the menu to select the last selected tab in that group."

I have uploaded a test version with that feature

0.4.1 => https://addons.mozilla.org/en-US/firefox/addon/tabgroups-menu/versions/