There will never be two sets of dot buttons (added by the system).
WTD had a look at one of my old libraries (
dgActionBar) which indeed is more a Command bar than a real Action bar (per Android definition).
Actually my dgAB can selectively display a logo, some icons and a 3-dots menu (or whatever) image/command. And you can have as many dgABs as you like on your Activity since you can place them freely in your layout.
So a way to fulfill WTD's needs (if everything works right) could be to place one or more dgABs on his layout, each sporting only the menu icon. At the same time the standard title bar would stay disabled (no need for it).
Erel's claim is absolutely correct (what did you expect? eheh) and it's to be noted that breaking Android's UI rules is never encouraged, but it's also true that each developer knows better about his/her own needs and goals, so a "think it different" attitude shoud not be blamed from the start (my 2c here)
udg