As people are coming and going, you have to either store PGP keys on some secure system where team members can't use it (as in export it for later use) or you have to regenerate it every time someone leaves.
I couldn't find any system for managing PGP keys without having local copy. For example webmail with PGP integration or PGP signing gateway would do; as long as users can't get keys, and you can manage user accounts for that system (to revoke access for members who are leaving).
If you have some kind of internal development team or some of your team members can write short program for that, adding PGP signing gateway to (authenticated, obviously) MTA is not really big task.