What about having Germany build a minor IC in Romania on G1 and then in Bulgaria on G2? If I’ve got the rules correctly, you can build 3 units a turn out of a minor IC whether the territory is worth big bucks or not. Bulgaria is very easy to take on G1 – you just walk right into it, and it comes with its own free defensive garrison. Like SZ 97 (Yugoslavia / Adriatic), SZ 100 (Bulgaria / Black Sea) is only two sea zones away from Egypt, so you can launch a direct attack on Cairo from transports built in Bulgaria. You can also launch a direct attack on the Caucuses via Bulgarian transports, or send mech. infantry and tanks north to support Barbarossa, or send infantry and artillery to invade Yugoslavia and Greece, both of which are immediately adjacent to Bulgaria.
Having ICs in both Romania and Bulgaria lets you drop six units a turn into the Black Sea – for example, a transport, a carrier, two destroyers, an infantry, and an artillery. You’re very close to Russian planes, but it’s not clear that the Russians can afford to take enough losses in the air to sink that fleet.
Bulgaria’s a weird gateway to Africa, but if you’re just looking to stick a German infantry in Cairo, it might be the best way to do that.