Taranto raid - I think the best way to support Italy is to present the best possible Sealion threat on G1.
You overkill the British fleets in seazones 111 and 110, sending everything you can at them except for two subs. Battleship, sub, and three aircraft off Scotland, two subs and 7 aircraft in the channel. The remaining two subs take out the Canadian destroyer and transport. If the British don’t scramble, then you should win all three battles without losing any aircraft in most of your games. Then you build a destroyer and two planes. The Baltic fleet comes out to seazone 112. Of course send the fighter to Rome too.
If the U.S. is not set up to counter the Sealion and Britain decides to fight the Italians instead of cleaning up your navy, you go through with the plan. You can have Japan hold off a turn. The British are now forced into another Atlantic naval engagement that pulls resources away from Italy. You walk away with one or two subs doing convoys in the Atlantic, fewer British fighters to defend Moscow, and a stronger Italy in the Med.