After gnashing my teeth a bit, I took a fresh look and approach. There were two things I noticed as I zoomed things out a bit. The first is that I didn't even realize the Soviets had a Tank and Mech Corps to the North that could play a key role in the operation. The second was that the German line is vulnerable NW of Stalingrad, east of the Don. So I tried it again and got a much better result. First, I punched a hole in the German lines NW of stalingrad and drove a tank corps through the gap. This presents a TON of problems for the Germans. It effectively removes the MOT on the N of Stalingrad from really helping to breakout and it forces a lot of wasted moves and units dealing with the Tank Corps, thus lessening the troops available to actual effect the breakout. Further, in a lot of my attempts, I never bothered to surround the German 22nd PZ division, but with the previously unnoticed Mech and Tank Corps, this because pretty easy. This guy will break his encirclement, but the key is that this division is not available to help break the main pocket at Stalingrad.
While I don't think it's perfect and can probably be broken, I don't think it's very easily broken and a lot of results would have to go the Axis way to break it. Further, in my experience mucking about with different variants of this, each time the Germans open the pocket, they are barely able to do so and most of the 6th Army remains pretty much trapped in place. They would surely be encircled again on the next Russian turn, but with so many axis units that can rail to the area on their opening turn, I doubt the encirclement could hold. The Axis just end up with too much stuff. Please note, that I haven't even looked at the situation in other areas of the map, so I have no idea what net effect such movement would have on the overall game. Please also note that it wasn't until I was taking the screen shot that I noticed the 16th MOT division way to the South. I think for purposes of my save file, you should assume that this unit is NOT available to assist in the breakout as the Russian units opposite could easily prevent this had I paid any attention to them.
Anyway, below is a screen shot of my attempt. I think it's pretty good, but not infallible. I've been looking at it too closely now and take a break for a few days and look at it again, as I'm at the point where i may be missing something very obvious! Perhaps someone else can take the ideas presented here and build upon them to get a completely definitive and permanent encirclement of the 6th Army. It was quite a mental challenge to even get it this far and I thank EvK for his AAR as it had me consider a new campaign and new tactical challenge with the game. If he hadn't done his AAR, i'd have never even looked at this. [:)]

Here is a link to the save file for those interested in breaking the pocket.
Save File
Curious to see it broken, how, and what improvements can be made. My thinking is that in 80%+ of games, it would hold.
Notes: I used ALT-CV when doing this as it took out a lot of the guesswork. I also had FOG off.
Matt