The limiting factor here is that the local jurisdiction would have the same computer problems that the rest of us do. They also would need a way to update thei

The limiting factor here is that the local jurisdiction would have the same computer problems that the rest of us do. They also would need a way to update their own clocks to reflect their own local time. So presumably it would be done within an existing framework, like defining a new time zone that is one second further from UTC.