I'd think the Allied air power is missing from this calculation. The air battle that winter & spring was more important than the ground battle& I'm thinking the Allies will have every advantage of OTL or even more.
I could easily be undervaluing the air power. I have never gone through the order of battle for both sides in North Africa month by month, so I could easily miss something.
But I think the bigger difference in our positions may be the assumptions. More specifically the assumptions about the POD. Early in the thread, there was a little bit about Malta falling, and other unspecificed minor things going right, then something bigger in October 1942. So from this I assume that a lot more of the Italian Merchant Marine is afloat than OTL in 1942. I tend to assume from the fall of Malta, the Royal Navy activity near Italy is lesser. I am trying to get a POD that is still recognizable as "Rommel has big success in Egypt in October 1942" but is as plausible as possible.
My feeling is that your POD is slightly different. So you get different results.
Now back to more specifics here. I am assuming a much bigger buildup of supplies in Tunisia than IOTL. I see much better/stronger German force than OTL in Tunisia, so I see the Allies being bounced back more in November 1942 and in the following winter. I see a stronger Italian Navy and more Italian merchant ships. And since the Axis are losing substantially fewer merchant ship in the 12-18 months before Torch, there are many benefits to supplies, air crew quality, and the like. Also, there is minor to no pressure from the 8th army. Due to whatever went so well in October 1942.
And for the last important issue. Strategic depth. IOTL, the Axis were trapped on two sides. Here, the will not be cutoff, but merely pushed into Libya.
So lets try another go at the TL. IOTL it was may 13th the Axis surrendered. So here, give the Axis only a 45 day improvement in performance. This means about July 1, the Axis forces are losing battles, and begin to retreat into Libya. Assuming they are not destroyed, it means that say the Axis have completed the retreat into Libya by August 1. The Allies are organized and supplied enough to think about attacking Sicily. Call it a September 1 invasion date is doable. And is this really the right date. A much better supplied Axis and larger Axis inflicts more losses on the Allied divisions. Do we have any/many Allied divisions going thru a rebuilding phase? Not sure. A lot would depend on how you saw each battle going. Maybe the Allies win quick wins. Maybe the have to beat there way thru some mountain passes. Maybe the equipment is in good repair. Maybe the Allies try to attack in multiple locations with long distance movement of men and equipment. Hard for me to say.
Now lets go to the big picture. The eastern med is shutdown. There is no supply benefit possible of running merchant ships in the Med Sea since the Eastern Med is Axis. You still have a large, but damaged Axis forces in Libya. It is not so clear to me that the USA does not decide to divert forces and supplies to support D-Day.
And here is the catch, say you do the Sicily attack. Move most of your forces out of Tunisia since Axis armor is running low on fuel. What is the big gain here?