To answer the question, I have a sys 4 that I toss the small parts in. I leave the rear rail attachment / hinge attached to the rail which is removed from the table as well as all the other stuff.
So I move the MFT/3, the guiderail, the fence rail, and one sys 4. Setup time is less than 4 minutes. The sys 4 also carries other Festool stuff like clamps as well as other frequently used measuring tools.
My tables mostly stay in the shop, but leaving the hinged bracket attached to the rail is kind of required if you expect the stops for the brackets to be useful. In other words, if you were to remove the hinged bracket from the rail, the stops will not longer be as accurate when you reassemble -- so, leave the bracket installed on the rail.