I am going to disagree here Kfsgo, Crete is not important because you (allies) could not support the island. It would become a big prison camp. My theory about the theater is this;
That doesn't mean it's not important, though; it just means that holding it (if you do) doesn't accomplish much until such a point as supply movements to it become less dangerous. Remember Crete has had a Brit occupation force from November 1940, though not a large one - they moved in after the Italian invasion to free up Greek troops to resist that. What are they going to be doing in this period?
Also probably disagree that it can't be supplied (with the caveat that I don't know what the shipping situation actually is beyond that supporting Greece seems to have been considered doable, if only just); in reality in June 1941 the nearest CW airfields are on the Egyptian border, which is about 300 miles each way; if the Italians aren't in Libya there's a whole infrastructure around Darnah and Benghazi available that cuts that down to 200. Not perfect, but it's a significant improvement - and of course it means aircover can be provided for more of the trip. Add to that the decreased need for aircraft carriers in support of Malta, decreased need for shipping in support of Malta, decreased need for aircraft in support of ground forces...you can build up a buffer in seven months, and Crete does have a military infrastructure up to a point - there are ports, airfields etc.
Hanging over all this of course is the spectre of Russia; that invasion starts June 22nd...or should.
France falls summer of 40. There are 150k French troops in western Africa, and around 100k Brits to the east of Libya. In December of 40 the Brits/French push into Libya and around 3 months later the Italians are kicked out. The way I come up with that is IRL, OConner with around 38k of troops pushed almost half way thru Libya in 3 months. Greece/Crete are now a side show with the Allies looking across to Sicily March 41. The expedition into Greece was at Churchill's insistence over the arguments of his generals. Now with the potential to knock Italy out of the war I think his generals would win the argument.
So Libya is over by March (or probably sooner, since I expect the French can get to Tripoli before Compass can get to El Agheila...). Conveniently that's exactly when the major CW force goes to Greece historically - there's no need to hold back insurance against the French in Syria (hell, they might send a few over themselves), so that can expand up to the availability of shipping to carry it, which is itself greater. What then? The Germans are going to take longer to get down to the Athens area, more troops are going to be evacuating Greece (and it seems sensible to send them to Crete rather than back to Egypt), so you've got a later start to a parachute-amphibious operation that was already pretty dodgy (and considered pretty dodgy) as is, now going up against a larger number of better-equipped troops. Very dubious - I'm not sure they'd risk it with Russia on the way. It'd make a great wargame scenario...
Don't agree that invasion of Italy is considered practical without the US involved - not in 1941. 1942, absent anything else to do...well, maybe, but 1941 dubious, especially with the armies Germany and Italy haven't just burned up in 1941-43 Libya and Tunisia available. Rather, I expect attention would have shifted to the Dodecanese - lots of opportunities to be 'busy' and try to draw Italian attention without risking too much.
December 41 the US enters the war and instead of Torch to North Africa, Torch goes into Sicily.
I can see that happening (assuming the urge to go straight into France can be resisted) - but it does mean the Med will cease to be an active theatre much sooner, with ship transfers consequent to that. Do we want that, rather than stringing things out a little longer?
As far as changes to where the LR planes go, there could be an arguement made that with the changes to events in NA, maybe the 9th(?) AF composition is changed to have another wing or two of heavy bombers. I am just not sure where you would get them from. The wings assigned to Hawaii are pretty much frozen and would take almost an act of congress to move them to the Med. The few MacArthur have are being used for Nav Search and bombing and I doubt you could get those away from him.
Well, the point is that it doesn't take much of a reduction to have an impact in this period (3/42-4/43, say) - slow down the B-17 replacement rates, delay B-24 arrivals by a few months, do both for P-38, whatever - the impact on the Allies' ability to defend places is pretty minimal but it reduces their offensive options. Remember the Japanese aren't starting from a 'Scenario 2' point here - so they've got (relative to what that gives them) a bit of a cross to bear, and another in the scenario being based off DBB with consequent reductions to supply production, support, engineers etc, and another in the French being involved etc - something has to give somewhere along the line or we're going to have some pretty short wars!