@oysteilo Much of the point of Middle Earth is that you skip the landings-from-London. The US comes to Gibraltar and supports the UK in attacking Italy.
A factory built in Egypt itself is typically not safe, and as you point out, the UK can’t really afford to fuel more than 2 factories for most of the game. So, you use the factory in South Africa, build one in Persia on turn 2, and then you have 6 British units per turn that you can use to secure Egypt, Jordan, and Iraq. This then lets you quickly send subs built in South Africa into the Med to start convoying Italy. If the UK can hold Egypt and Jordan and bother Italy with subs, then Italy will usually be far too poor to resist a strong US invasion; the US can buy whatever transports, land units, destroyers, carriers, etc. are needed, while the UK buys only the relatively cheap infantry and subs, plus maybe 1 tank in South Africa now and then. This makes the best use of the larger US income and also sets the US up to ‘fork’ West Germany, Normandy, and Italy from the sea zone next to Gibraltar.
The thought behind Middle Earth is that you usually need to invest something in the Med/Africa in order to avoid losing most of the British income, so as long as you’re playing there at all, you may as well go big in that theater. Better to just keep on pushing in the Med / Middle East than to try to pivot to an Atlantic strategy that will require substantial UK investment in many transports, destroyers, carriers, and so on. As @oysteilo correctly points out, you want to keep UK investment in infrastructure to a minimum…but you start with harbors in South Africa and Egypt, so the only infrastructure you need to buy for Middle Earth is a single minor factory in Persia and two transports (one at a time) to shuttle troops up from South Africa to Egypt. Total investment is 26 IPCs. It doesn’t get cheaper than that, as far as effective strategies go.
As @Galendae correctly points out, the strategy can lead to extremely long games against a competent Axis player; if the US needs to spend most of its income containing Japan in the opening, then a serious US invasion of Italy won’t come until much later in the game, by which point Moscow has probably fallen or at least been crippled. I don’t see a good way around this, which is part of why I prefer to play Anniversary these days rather than Global.
I’m curious if anyone can recommend other UK strategies, especially if they’re likely to lead to a shorter game. There was some interesting discussion of “Gibastion” a few years ago, but I haven’t heard of new ones since then.