I have been contemplating the 1Dx v 1Dx2 vs 5D4 question myself and have spent considerable time reading in-depth reviews and talking to people with experience of both. I have rented the 1Dx2 but not used the 1Dx and the general idea I get is that the 1Dx2 is a 'significant' step up if you are already pushing a model like the 1Dx to its limit: the 1Dx2 provides about 1-stop better ISO performance, it drives big whites+extender better. If those will overcome limited focal length then fair enough. You already have the 1Dx so you are the best judge as to whether the 1Dx2 will offer more opportunities for you, but given the tenor of your original post it seems focal length is now your main concern, not AF accuracy, and the 1Dx2 will not solve that.
In your OP you say
I find shooting either distant wildlife (mainly deer) or motorcycle racing and coming up wanting to have more reach than I have today.
Yet you are now talking about upgrading the 5D3 so I would ask whether you really know what problem you are trying to solve. The 500 f4LISII plus tc plus 1dx2 will give you more reach and higher keeper rate - but that is no good if your current porfolio shows you need 600-840mm instead of 500-700mm.
If you are wanting to handhold the lens a lot then the 500mm makes far more sense.