I drew the Lahkmids into Persia for the sake of simplicity, but technically they are a loose client state and not a proper part of the Empire. They wouldn't be Muslim... but they would certainly be a competitor. 

Also, alternatively, if you find someone not on the map while you are researching and you can place them in this period, I would allow you to play them. If you find a sub-tribe amongst the Quryash that you would want to play, you can probably request Aaron for control and figure out where they would go. One of the nice things about going to the level below nation-state is that we can add things without fucking with national sovereignty.