Going through the med is just impossible in pretty much any game. Either Italy or Germany is going to sink that transport with planes.
So with that reasoning, you must hope for a J1 declaration of war on the US, and then you could do this:
US 1: Buy 5 fighters. Sail your single atlantic transport 1/4th toward Saudi (SZ 87)
US 2: Buy 5-6 bombers. Sail transport 2/4ths to Saudi (SZ 82 or 69). US 1 fighters to French West Africa.
US 3: Transport now 3/4ths to saudi (SZ 71). US 1 fighters to Egypt. US 2 bombers to French Equatorial Africa.
US 4: Go time.
Hit Saudi with your transport. Send in 5 fighters and 5-6 bombers from Africa, taking bomber losses.
US 5: Build factory (and an air base couldn’t hurt), land your planes on it or near it. If Iraq/Persia are still available, take those if possible.
US 6: First turn you can purchase units in Saudi Arabia. Buy factories in other middle east countries, if available.
This is about the time Moscow has gone to hell or the Germans are coming into the middle east. Not enough time to really get any ground units over there. But you could build fighters on US 3 and 4 that would arrive US 5 and 6 for a respectable plane stack. With a bit of UK help, probably enough to shut down any hope of Moscow or the middle east being seriously threatened. A huge problem with this is that you’d have +8 Germans or Italians coming from Turkey.
This is a 100% Atlantic buy for the first 2 turns turns and a significant drain for US 3, 4, and 5 as well. Very dangerous. Japan is going to go nuts because, remember, they J1’d you.
Seems like a crazy damn idea–one that is too crazy to work well, probably. Not only that, but it’s completely obvious what you’re up to. However, I think it’d be pretty easy to have UK prevent Japan from killing/blocking your transport J3. And if Japan invested too much in the Indian ocean to stop you for sure, then they’re ruining some of their J1 momentum, so maybe that’s not entirely awful.
I guess you could also send your pacific transports through the panama canal, building a naval base there. This would give you four more units in the middle east shortly after your first transport arrived.
Better alternative, with nearly the same effect:
Don’t do Saudi, just have UK save you Persia/Iraq. This saves you from having to violate neutrality, and both are reachable on the same turn as Saudi. If you do hit Saudi, do it the next turn, saving the neutrality violation for one round later.