IMO, Sardinia&Corsica. Properly executed, it could lead to Italy switching sides, securing the Alpine passes before the Germans send significant reinforcements, whilst 4 crack German divisions get stuck on Sicily
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More likely the Germans entering Italy would have reversed course & fled north. Leaving the Italians in the south unmolested. The italian government may have been able to preserve a effective rump army since a sizable portion of the officers in the combat units would not be German prisoners. Most of the conscripts would still desert & go home, but a better cadre could exist if the Germans have to flee and do not have time to disarm & decapitate so many Italian field units.
How far north the Germans would go before rallying I'm unsure. They might try holding the mountains protecting the Po River basin & the industrial region there.
When in 1943? The allies have the ability to do more than one, apart from the cross-channel option.
Heres my notional alternative TL. Items marked * occured OTL tho they may be somewhat modified by butterflies.
Jan 1943. Symbol confrence; Allied leaders decide to make Tunisia a holding action, hoping the Axis send as many ground & air forces as then can into a strategic trap. Airforces operating out of Algeria, Lybia, and eventually Tunisia will with the navies endeavor to isolate the Axis armies in Tunisia.
*Feb//March 1943. Axis offensive in Tunisia savages Allied ground forces, revealing leadership failures and highlighting emerging problems in Allied equipment, training, doctrine, and attitudes.
Late March 1943. British Corps from 1st Army invades Sardinia suprising Axis leaders. The two weak Italian divisions collapse & the half formed German formation present flees to Corsica & then Italy. A combined French/US Corps leapfrogs to Corsica. *The follow up force of airfield engineers and airbase ground support for a US/French air force outnumbers the Allied ground forces. in 60 days some 3,000 Allied aircraft can be based on Sardinia Corsica & more air base capacity is under construction. (This last occured OTL from November 1943 through early Jan 1944.)
*March/April. Axis air losses in the Mediteranean become unsustainable & air strength falls to under 1,500 effective aircraft. Allied airstrength reaches 4,000 effectives & continues to grow. Axis support for the Tunisian position effectively ceases in April.
For political & personal reasons both hitler & Mussolini refuse to recognize the need to evacuate Tunisia. By mid April it is to late as he Italian transport on land & sea is crumbing under Allied air attack & by May Axis Army Group tunisia has lost all offensive capacity.
April. The Facist Grand Council is actively considering how to eliminate Mussolini & create a better 'situation' for Italy. Withdrawl of italian forces from the east, France, and portions of the Balkans is started. Germany starts slipping 'reinforcements' into Italy.
April - June. Allies have spun up deception operations aimed at drawing Axis forces to the 'non targets'. 8th Army has prepared plans for operations against the greater Greece region, the Dallmation coast, & the Italian boot. 1st Army has plans ready for ops against Sicilly & Italy. HQ 5th Army plans for US support of 1st Army. HQ 7th Army & the French are under a single army group HQ preparing plans for southern France = seizing the Marsailles/Toulon port group & establishing a lodgement there.
*May. Allied air control over Tunisia & south Italy allows protected convoys to pass the Mediterranean. Preparations to do so start.
May - June Axis AG Tunisia collapses from lack of supplies Allied holding forces. *Allied cargo convoys begain running from the eastern to western Med. Italian navy refuses to interfere.
*Recently activated COSSAC dusts off old Sledgehammer plans & starts a new round of planning for invading NW Europe.
June/July. Mussolini is removed from government. New government begains negotiations with Allies. Germans figure it out & increase efforts to take control of Italian territory. Italian forces still withdrawing to Italy are stalled along the way. Germans threaten a counter coup, Allied armies invade central italy to 'protect' Rome. Italians surrender. Secondary Allied invasions come to Sicilly & Taranto region.
August. Italian Front temporarily stabilizes in north central or north Italy. Allied 6th AG continues planning a larger invasion of S France. 8th Army prepares further plans for the Balkans.
Aug - Sept. The ground portion of Op Bolero is restarted & a trickle of ground support forces arrive in the UK. The air portion is accelerated & the US plans for activating two more air force commands in the UK in by 1944.
Sept-Nov. Allied efforts to break the German defense in italy have mixed results. Allied disagreement becomes stronger with Churchill & Brooke arguing for a main effort in the Med. Including in the Balkans. This comes to a head at the confrence in Terhan. Roosevelt & Stalin come down firmly for France as the main effort. Churchill is disappointed & keeps bothering people about a operation against Trieste. Eisenhower is named Supreme Allied commander.
December 43. Ike pulls the trigger on the Anvil operation. By new years a Allied army is building up on the Riviera & isolating Marsailes. Italy is turned into a holding or pinning operation & the 6th AG has priority for material & men .
Jan 44. Ike tidys up the Med, send the Amphib fleet to the UK & heads off to prepare for the invasion of northern France. Op Bolero is in full swing, but a portion of the forces are directed to 'Bolero South' = 6th AG. Overlord plans are expanded from a three to a four division assault.
Feb-April. Germans flail about attempting to reinforce failing battle fronts, and leaping after the shadows of Allied deception ops. 6th AG expand & now includes a Commonwealth army. Op Bolero runs its course & the Allies can boast the strength of two army groups either in the UK or on the docks in the US. Late April 6th AG & AG Italy kick off offensives to pin German forces & draw in reinforcements.
Early May. Op Neptune is executed with a solid beachead established between the Vire & Caen. Defenses are incomplete & undermanned. The prefabricated ports the Allies bring allow a rapid build up. By June the battle for normandy is over & the new 21st AG starting to push into the interior. 12th AG splits off & attacks south to capture Brittiany & its ports.
June - July. Germans attempt to fight a mobile battle on the French interior plains. Under crushing Allied air attacks this fails & a effort to make sucessive delaying actions turns into a rout & rave for Germany.
August - Oct. Allies close to the German border & puncture the fortifications in the center & south and cross the Rhine in the north. Only supply transport problems prevent them from advancing further.
Nov - Feb. German attempts at a counter offensive cause a lot of casualties, but sputter out soon. The Allied punctures of the West Wall defenses render it useless. Multiple crossings of the Rhine occur & despite the weather. By late February multiple advances are fanning out from the Rhine bridgheads & German armies are falling apart. Late Feb Op Eclipse decapitates the centralized command & German armies are surrendering to the west Allies enmass.