A ZD1200 needs to be factory reset as the admin credentials have been lost. My questions is will the AP's automatically reconnect once the ZD1200 is set up again?
If everything is on the same subnet the APs will discover any/all ZDs on that subnet and join the ZD that has the most available licenses. If you want to keep the same IP that’s fine but if you want to change it, then that is fine too. The APs will discover and join the controller in either case.
If the APs were on different subnets, then the easiest solution would be to use the same IP because the LWAP discovery broadcast works only for all devices on the same subnet. If you wanted to change the controller’s address in that case you would also need to change the L3 discovery mechanism that’s in use (DNS of dhcp opt 43).
Who would ever CLI to individual AP's and do a set director or set scg command? You would only use those commands in the case of a L3 deployment where there is no ability to create a DNS record or DHCP option 43, or where you have multiple controllers or a mix of ZDs and SZs. That's the only time those commands would be used. He has a simple L2 network.
If the previous admin did do a set director, then all Nathan needs to do is factory reset the APs and they will then find to controller at whatever address he chooses. He has already concluded that he has to factory reset the controller and rebuild everything from scratch. If it was me, I would not keep or trust anything setup by the previous admin who didn't have the common sense to document the config or pull backups.