5D-D600-D800

I agree with most of what you said.

Did you also try D800 + 70-200VR2 combo?

I have both combos and they are really a very close in AF performance.

One aspect of 5D3 AF that I've found deficiency is on autofocus point selection.

It consistently picks closest focus point(s) in the focus group while on D800 it can lock into correct subject based on color, shape or subject contrast.