In the situation that I was in -- which is what this thread used to be about -- my problem was that the surface I was stuck on/in was super-slippery (slick mud on ice), not deep, thick mud. There was nothing dynamic about the pull out -- forces were moderate. I bet the forces were no greater than if I had been towing a big stock trailer by that ball.
Yes, about that situation you were in:
1) From your pictures, your description, the other poster's pictures, and the location of the "scene of the crime" I pinned down on my Benchmark Atlas, it's clear you were on a dead-flat section of two-track, probably that east-west two track running between NV 214 (Leonard Cr Rd) and Pinto Mtn/Pinto Hot Springs. So, no real slope to add to the forces. The relative absence of force needed to extricate you seems to confirm there were no issues as to chain/strap/attachment point failure, and also makes me think your limited-slip isn't working, a common situation on older Superduties.
2) What was your tire air pressure when you got stuck? Did you air down prior to the attempt to negotiate the crossing? After getting stuck, did you air down as you tried to self-rescue? I run Load Range E tires on my Superduty and I imagine all or virtually all FWC and similar camper jockeys do, as well. High load capacity tires derive much of their rated strength by being inflated to or near to the maximum PSI embossed on the sidewall. Trouble is, that's the reverse of the approach to negotiating soft ground, be it mud, silt, or sand. It's always risky to air down a heavily-laden truck, as one can much more readily pop a bead or cut a sidewall while the tire is pressurized less, but sometimes it's the only logical move to make. Carrying a high-quality, 100% cycle rated air compressor makes re-inflation following the problem crossing easy, which in turn makes the decision to air down easy. I carry the aforementioned compressor as well as a simple tool for airing down, so I can reduce my tire pressure and re-inflate, recovering the full load capacity as well as puncture resistance on the far side of the creek, in a matter of minutes. The compressor also makes self-rescue in the event of a puncture feasible, provided you've got a good plugging kit on board.
3) Messing around with the tire pressure DOES encourage me to want to run 2 fullsize spares when Wandering the West, at least the NV-OR-ID parts of it.
4) I forgot to ask: Did you get to Pinto Hot Springs following your extrication, and if so, is it a soak-able HS?
Foy