I think the GA should make a clear announcement before boarding that s/he will be enforcing zone boarding and to please respect the zone printed on ones bp. If anyone requires pre-boarding or wants to request a boarding earlier than the zone printed, please approach the podium with your request.
Then firmly but politely reject anyone who gets to the scanner before his zone is called.
The *only* exception I'd make aside from those who came with a request would be to allow a party traveling together to board with the highest priority, even if on different PNRs. (The spirit being a couple traveling together, not a family of 8.)