What if the Afrika Korp destroyed at the Battle of Gazala?

I have been reading Raising Churchills Army by David French and on Page 219, I came across this

"Had it not been for the efforts of the Ariete and Trieste in overunning British postions and linking up with the DAK on 28-9 May, and the work of the Italian X Corps in opening a path through the British minefield DAK might have been destroyed in the Cauldron"

Simple question If the above efforts had failed and this led to the destruction or surrender of the DAK, aside from the obvious propaganda boost, what effects would this have?
 
Is this in 1941 or 1942?

-Earlier invasion of Sicily.
-More American resources go to the Pacific--less of a "Europe-First" strategy. Solomons and New Guinea campaigns go faster.
-More troops and guns will go to Russia.
-No Operation Torch means American troops are inexperienced and probably perform poorly in Sicily and Italy.
-If Rommel gets captured, then Guderian's plan of fighting an Allied invasion of France with massed armor rather than coastal defenses might come closer to reality.
 
Is this in 1941 or 1942?

-Earlier invasion of Sicily.
-More American resources go to the Pacific--less of a "Europe-First" strategy. Solomons and New Guinea campaigns go faster.
-More troops and guns will go to Russia.
-No Operation Torch means American troops are inexperienced and probably perform poorly in Sicily and Italy.
-If Rommel gets captured, then Guderian's plan of fighting an Allied invasion of France with massed armor rather than coastal defenses might come closer to reality.

Late May- early June 1942.

No Monty in charge of the 8th Army, which could have some interesting effects later, though he probably would have still risen to become an army commander somewhere.
 
Big British victory in June 1942 will go nicely with Midway and provide a huge morale boost especially as the Germans score some big wins early during Case Blue.

British will likely be able to push the Axis out of North Africa before Operation Torch. Torch will still likely go off, but might be more aggressive since opposition will be limited (Tunisia is included).

Plans might be made for a quick invasion of Sicily afterwards, and the British might forward plans for actions in the Aegean. The US troops might perform worse in Italy, but if quick enough moves are made, Italy might choose to defect just as the Germans are wiped out in Stalingrad. Lots of unknowns to what happens in Italy in the winter of 1943 depending on events in December 1942.

The question is whether the British are able to talk the Americans out of attacking France in 1943.
 
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