In my experience the shuttle dragons typically just do a verbal check and don't insist on looking at your BP. Just tell them you're going to terminal A, then get off at B.
It's as simple as that. *No one else* will question you - a boarding pass gives you access to all terminals at EWR. TSA doesn't care, and neither do the lounge agents. The bus policy is nonsense.
Coming back to C, though, there is no option besides exiting the terminal and riding the train. And that can take a while. Realistically, the pain of getting back to C may outweigh the perks of the Lufthansa lounges.