Update
So, Mansa is just a turn away from rifles, however Djenne (holy hinduist and statue of lib) is two turns away from my cavalry and is guarded by a couple longbowmen only. I send all my seven relatively healthy cuirassiers to attack it. BtS AI upgrading is costly, also upgrading removes the fortify 25% bonus, which means there's a chance to capture the city against a fresh rifle or two.
Meanwhile, I realize all American culture is gone, along with my war weariness, to be replaced with Mali influence. Boston and Philadelphia are 100% Malinese and have no conquest immunity to Malinese culture flip because I captured them from the Americans. I go straight to building culture, there's no time to wait for buildings to pay off. Culture flip % depends on the number of nearby tiles with dominant foreign culture, so expanding to 100 culture to get the hidden +20 culture/turn per tile is vital.
There's no time to complete Rifling and upgrade to Cavalry. Instead I switch research to Corporations planning to revolt from Mercantilism to Free Trade as soon as I get the bonus trade route. For now, I revolt from Nationalism to Bureacracy to maximize the commerce in the new capital, Numidian.
Next turn, Mansa brings numerous reinforcements in the conflict zone, including some airships. I advance one more turn and get to Djenne in hope the AI will empty it of some of the units. but it's not to be. My disappointed cuirassiers pillage some towns to the ground and then I sue peace, getting some money for it.
Suleiman asks me to convert to Judaism, and I agree (for 5 turns only of course). Since now we're freindly and he's out of the war with Mansa too, we sign Defensive Pact as well.
The Pact is not very popular with my other allies, nor is my trade of Divine Right to Mansa for ~500 gold. Whatever. My spies report Mansa can research Electricity in 15 turns or so, meaning my research rate is about to surpass his. It's Scientific Method after Corporations, and now we're turns away from Biology.
The two GP I had plus a new great scientist build two academies in Constantinople and Numdian and the great prophet settles in Numidian.
The Byzantine empire adopts Free Trade and Hinduism. Su agrees to convert to Hinduism for Replacable Parts and I agree because I need him friendly.
Scientific Method reveals everyone has oil *sigh*. Nevertheless, Angora starts on a settler to claim an extra oil for my empire in the jungles north.
The old and the developing new capital:
Empire overview 1330 AD
p ) and it makes good use of Byzantine's UB (one of my favourite as well 
). You'll probabely have to delay war until you hit Industrialism for Tanks and especially for Marines as you really can use them. Invading MM is not such a great idea since you don't have a techlead over him and you have to build up your economy first. I don't know exactly the diplo/tech situation as I didn't look at the save but I'd say you could start by taking (protective 
) Saladin because he seems to be backwards. He has some coastal cities which can be taken simultaneously. That gives you a foothold on the other continent and opens up several ways to attack Cesar; again coastal attacks as well as 1-2 SoDs rushing throught his inland cities. Then taking Boudicas land wouldn't be much of a problem. If you look at the Victory screen, you can see whether you need to attack MM as well for the land (not sure if you'll need that..).
but on the other hand, it wouldn't make use of the diplomatic situation..
goes to Domination 
