It looks like the firmware on these new IAP-305's is 6.5.4.3. I had to factory-reset one of the devices and then connect it to a network with no other Aruba devices, which allowed it to behave as expected. It doesn't look to me that the old IAP-105's can be upgraded to this firmware.
So, looks like what happened is that these new IAP-305's tried to get their settings from the IAP-105's with the old firmware and then ended up bricked until a factory reset could be performed.
Just to be sure, does anyone know of a way to get IAP-305's and IAP-105's on the same firmware version?