You have tried several D600 bodies and TC’s and now the D7100. All of the bodies and TC’s seem to work fine with other lenses and the 500mm lens works fine without the TC on all body and with the TC’s on a D3s and a D800.
The one piece of equipment that has remained constant is the lens. No one has responded to your other post in the AF lens forum so you likely have a unique problem.
Maybe a trip to Nikon for service for the lens, TC and camera body is in order. Have you contacted Nikon about this issue yet?
I will PM a Nikonian who has the 500mm lens and a D7100 and point him to this thread.