I imagine that the carriers could be more than just passive stations that can move every week. When controlling a carrier, you could be given an orrery map of the system that you are in, with markers for the various POIs (with maybe a scan limit of 100,000ls or so). A carrier could select any of these, and aid in player operations by dispatching limited numbers of NPCs or by using a small amount of fuel jumping to it directly in the same manner as a capital ship to any destination within a star's influence. Secondary stars would have to be jumped to using much more fuel and prep time for the jump (several hours so as to not ruin hutton orbital) and other systems would probably have to be done on a weekly basis through fleet goals of harvesting jump fuel.
Fleet carriers could contract directly with system minor factions to make whatever their current operation profitable, be it combat, or mining, or piracy. My intention is to make some of those activities massively profitable through faction contracts. Fleets would take on a percentage of ship insurance costs for their NPCs, so there is some risk in performing unsuccessful operations, and the carriers would have to have weaknesses just as capital ships do to add risk and prevent farming.
You can create squad goals to deliver materials to it for different end of the week functions like jumping, adding services, maybe aesthetics, so that eventually with a lot of work it can be as functional as a station. With enough work you can jump it out somewhere far away, and perhaps if enough fleets follow suit you could make a little bubble of sorts.
In order for us to effectively take them outside the bubble fdev would need to give us the ability to harvest and synthesize our own cargo. For example surface extractors, and for stuff like hydrogen fuel just let us scoop and turn it in.