"I would suggest resetting camera to factory and clearing all custom settings ..."
I advised this a long tome ago. It is what you need to do next and first off. I have only used a 1DX Mk II a few times but I use my 1DX all the time. Unless something was drastically changed between the two I don't see what you are. Either that or the ef 500mm f4 is a unique lens and I don't have one to try for you.
The biggest lens I can put on my 1DX right now is the Siggy 150-600mm S. I set the Av to f16 and ISO to 100. The camera selected a SS which would be impossible for me to accomplish a sharp picture (1/30, 1/15, etc). Well below the 1/600 you would have expected if your thoughts were correct.
When I set it to auto ISO (min ISO to max ISO) and had good light the 1DX did seem to try and stay at 1/500 (600mm lens) which you might expect. However, when I pointed it to a really dark place the SS went very slow as expected. So slow you could not get a sharp picture. Do the reset.
EOS 1DX and 1D Mk IV, even less and less other stuff.
