The only option I'm aware of would be to create an out-of-unit membership record for each bishopric member in each of the stakes (except for the stake where their actual membership records are held). You may also need to assign them to a standard calling in those stakes. Unfortunately, this may take a lot of coordination to set up, and to update when bishopric members change. And, unless they're put into a leadership calling in those stakes (such as a clerk), they may not get access to the tools they're hoping for anyway (they wouldn't be able to access Leader and Clerk Resources for Send a Message or membership reports in those out-of-unit stakes).
Samuel Bradshaw • If you desire to serve God, you are called to the work.