AH Challenge: Fortress Stalingrad survives

So alot of people can agree that Hitler's obsession with taking Stalingrad didn't help the Germans too much. Alot of TL's with the Germans winning victories in 1942 involve either more German focus on Baku than Stalingrad, or if they do still attack it, the 6th Army managing to escape and be reused at Kursk or some other battle. But how could the Germans save not only the 6th Army, but end up taking and holding the city itself, with a POD after the Soviets surround the city?
 
some how a distracting move on moscow and baku has to be made to relieve the 6th. plus resupply would be a HUGE problem. fast light supply brigades might work.
 
The Germans held about 80 per cent of Stalingrad at the time the 6th army was encircled.If Hitler had allowed the forces of Army group A particulary 1st panzer army to augment the forces already commited to Mansteins Relief operation[Operation Winter storm] there is a Chance for German Success.Winter storms success would have blasted a relief Corridor through the Soviet lines,allowing the Re-Supply of the 6th army.The Soviets would probably launch a scaled down version of Operation little Saturn,while concentrating their main forces on crushing the German supply corridor.
Provided that the Germans hold the Corridor through the winter,Mansteins panzers could conceivably be in a position to turn the battle mobile,forcing apart the jaws of the Soviet encirclement and forcing the Red army back to its Start lines for Operation Uranus.Axis casualities would be enormous,but Hitler might then decide to have one last crack at Capturing Stalingrad in spring of 1943.Throwing everything against the Soviets in one last surge its possible that Stalingrads defenders buckle and the Germans take the ruined city.Considering the scale of losses I don't know what they would do next,but with Hitler in charge probably something stupid.
 
Who knows but it would be highly symbolic that he managed to take the city bareing Stalins name
 
So a lot of people can agree that Hitler's obsession with taking Stalingrad didn't help the Germans too much. Alot of TL's with the Germans winning victories in 1942 involve either more German focus on Baku than Stalingrad, or if they do still attack it, the 6th Army managing to escape and be reused at Kursk or some other battle. But how could the Germans save not only the 6th Army, but end up taking and holding the city itself, with a POD after the Soviets surround the city?

I don't see the goal as you stated as particularly viable ... however ... if you assume that the Soviets take heavier casualties in the OTL 19 November operation and also that the secondary operations in late November and early December are less successful and incur heavier casulaties than OTL, then you have the possibility of "Winter Storm" (Manstein and Hoth's attempt to relieve Stalingrad to allow 6th Army to withdraw) being more successful than in OTL. That would alow 6th Army to withdraw from the cauldron-- still probably without the great majority of their heavy equipment bearing in mind tghe fuel shortages 6th Army had -- and meet most of your criteria. in this scenario, 6th Army would still be pretty much useless and need full re-equipping and also have taken significant casualty levels and also need significant reinforcement and retraining.
 
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