Here’s how I would do it:
Don’t think of the new power as just “Italy.” Instead, think of the new power as “all minor Axis powers.” The starting territories would be Italy, Southern Europe, Algeria, Libya, Rumania/Bulgaria, Finland, French Indo-China Thailand, and Argentina (!). You can actually leave the starting unit setup as is – that will give the new player 2 fighters, a battleship, and a transport to start with, while still leaving Germany and Japan with a bomber and five fighters each.
Open the Turkish Straits.
Put Italy first in the turn order, e.g., Italy - Russia - Germany - UK - Japan - USA. This is OK because Italy’s not really in position to mess up the Russian starting units too badly.
Leave Italy at 3 IPCs, and create a new 2 IPC territory out of neutral “Peru Argentina” that starts out empty, under Italian control, just as Brazil starts out empty and under American control. This will give Italy 14 IPCs at the start of the game – enough to buy a carrier, or a fighter, or a bomber, or a cruiser.
It’s OK that Italy has only three production slots, because Italy’s going to want to drop some expensive air/sea units. For example, if on turn one Italy builds 3 infantry and saves 5 IPCs, then on the next turn Italy might have as much as 22 IPCs to spend – which is really easy to do; you could buy a fighter and a bomber, or a transport, a destroyer, and a tank. Having only three production slots doesn’t really cripple the Italian player, and it wouldn’t be realistic anyway for Italy to crank out enormous armies of infantry; Italy’s population just wasn’t that large. If you really want to, you can probably build an Italian factory on turn 2 in Rumania.
