Upload & Sell: On
No doubt that the 1Dx is the current apex of the long 1D line. It is clearly a fine camera, and truthfully I'd buy one if I had the capital. Having said that, there are 1,000s 10,000s? of PJs and sport shooters working the 1DIV every day with professional results. It is still an excellent camera. My main attraction to the 1Dx would be its higher ISO. A step or two improvement seems to come with each generation. A useable 51200 would be a godsend to me with the dark venues I work. The 1Dx appears to have better AF (though disputed by some) and the second CF card is long overdue improvement.
Having said all that I would in your situation question the cost/benefit of the 1Dx purchase vs say selling the 1DIII and moving to a 1DIV. I think 1DIVs are in the $3200 range right now. Don't know what the 1DIII is going at. $1500? So you'd be looking at ~ $2000 cost to upgrade to the 1DIV. The 1Dx is still ~$6,000, so your cost to upgrade would be maybe ~ $3500. Big question. Is the 1Dx worth $3500 more than the 1DIV to you? For me (aside from the fact that I just don't have the capital), I don't think the 1Dx is that much better than the 1DIV. Others likely will disagree.
If you went with your 5DIII you'd have the latest technology in high ISO, processing, handling, and have a truly robust and completely useful action camera in the 1DIV. $3.5K goes a long way towards buying some nice lenses.
I think Jim's experience noted above is particularly useful to you. Yes, he likes the 1Dx better. No he didn't think the cost of upgrading resulted in greater benefit. You'll have to work your own numbers and situation.
For me, I've held at a 1DsIII and a 1DIV as the best cost/benefit outcome. I don't have the latest/greatest of anything, but bluntly 99% of the time if I don't get the shot it's me, not the camera.