Ouch. So sorry to hear about this. Sounds like the catching and moving of the tangs was just too stressful on them. The big yellow can recover from the popeye, but needs good water conditions, good diet, and no more stress in order to do so.

This is why most folks won't sell their fish until the live rock and corals are removed from the tank, because it's just so difficult and stressful. Once the rock is out, you can just syphon the water level down until the fish are easy pickings. Again, really sorry to hear about this. Must be very frustrating.