I thought of one way as a workaround:

1. Save each livery as a separate folder, thereby creating a unique EFB batch of folders/files for each (example: Save a UAL version, an AAL version, etc).

2. Name the tags/folders for the generic EFB configuration (the buttons) something generic, like: Base Airport, Base Departures, Base Arrivals, Base Approaches, System Airports, Destination Airports, etc, etc.

3. Decide upon ONE base for each airline (I would choose KIAH for UAL, KDFW for AAL, etc).

4. Place all the charts, etc for the base airport you chose in the ...EFB/Base Airport, Base Departures, etc of the aircraft you are setting up.

5. Place airport diagrams for all other hubs for that airline in the ...EFB/System Airports folder for that aircraft.

6. Fill in destinations and other charts/folders as you choose.

This way, you could have a unique set of docs for each airline flown.  HOWEVER, you have to use generic names still for the folders/buttons, and I'd rather create unique ones for each aircraft if possible.  

Haven't tested this, but I think it should work unless the aircraft folder name cannot be changed without messing something up.  :-/