I think our best bet is this: Wait for all the troops from Bapedi, capture Zimbabwe first. Then, if we have enough left, go for Ulundi. Leave Intombe; it can wait, and it will ensure the Zulu don't get wiped out before we have a chance to get peace concessions from them.
Inherited turn: Bapedi's citizen assigned to work, Teotihuacan assigned to the wines tile.
330 BC: I spread out the jaguars around Zimbabwe's food tiles to prevent the city growing to size 7 before we can attack it.
Interturn, an archer attacks one jag and loses.
And Cleo captures Ulundi! Well, that makes it obvious what we need to do. (Is it dastardly to form a blockade within Zulu territory to block Egyptian units?

)
310 BC: Workers complete a road to the edge of Zimbabwe's radius. Five jaguars from Bapedi move outside Zimbabwe. I have 24 jaguars available to attack next turn. And, um, Egypt somehow has a sword and a chariot near Intombe on our peninsula! Must have sailed there.
Interturn, I watch another Egyptian boat land units near Intombe. America completes the Great Wall.
290 BC: This is it. The grand assault on Zimbabwe begins. 24 jags and one spearman can attack.
Lost 10 jags.
It would take about another 6-7 turns to get enough military over to assault Intombe, and by then Egypt will probably capture it. So we dial up Shaka.
He should be conceding everything he's got for peace, but he won't. It looks like I can only get about 2 techs! So, what to take, what to take. Well, the reason the techs are so expensive is because we only know two other civs. But I can only get one contact, or I can get Map Making which will get us at least one contact and probably more.
So, our inflexible demands are Mpondo and Map Making. I can't get a contact along with those, nor can I get the World Map. What I can get is Philosophy, a worker, and 27 gold. Peace is made.
Mpondo turns out to be a useless joke of a city. I was hoping it had a lux or something. Well, maybe it has coal. At least it's more unit support; we're now at 32 allowed, 35 total.
Tenochtitlan immediately whips a galley (I had swapped it off jag last turn and it had 10 shields in the box.) Madrid swaps to settler to fill in the old dot south of Tenochtitlan. The fishing villages start harbors, of course. Zimbabwe starts a temple.
Heh, we control the Oracle without even having the tech to build it!
Zulu will pay us 1/turn for an ROP; may as well take it.
Interturn, an American galley sails by.
270 BC: Our galley sails out and finds the Iroquois. Both of these new civs are slightly behind Egypt on the power graph, and have no deals we can make with them.
Interturn, Egypt destroys the Zulu.

smoke: ! I should've thought to pay the Zulu gold-per-turn for tech. That doesn't hurt your rep, right?)
250 BC: Whip the harbor in San Antonio. This is so we can start trading our wines.
Interturn, Egypt moves three war chariots from outside Intombe next to Teotihuacan. Are they just passing through, or attacking?
230 BC:
Trade Wines to Egypt for Contact with China and Iron Working. Surprise, we have no iron.
Trade Wines to America for Literature + Mysticism.
Trade Literature + World Map to China for The Wheel + Territory Map. We do have two Horses!
Trade World Map + 10 gold to Iroquois for their Territory Map.
Trade our last Wines to China for Mathematics.
Pay Egypt 6/turn for Furs to replace the Wines.
Trade 185 gold to Iroquois for Polytheism.
Trade Polytheism to China for Code of Laws. (A typical buy-one-get-one-free tech deal.)
Our Golden Age ends. I start a minimum-science run on Republic. Egypt already has it, though.
Interturn, Egypt's chariots fortify but don't move...
210 BC: Whip temple in Zimbabwe. (Surpisingly, the city didn't have any whip effects when we took it over.)
Interturn, Egypt demands 21 gold, and of course we pay. Their chariots go on by.
190 BC: We continue bringing irrigation home.
170 BC: zzz
150 BC: Bogota is founded two squares south of Tenochtitlan, putting us neatly at 36-of-36 allowed units.
We have a spare Horses but nobody needs it.
The two libraries are prebuilding for either aqueducts or marketplaces; whichever tech we manage to beg, borrow, or steal first. We also need a government tech when we can get it. Everybody but China has most of those techs, but only got them in the last couple turns. China's as far behind as we are.
But we're definitely back in this game, baby!
http://www.civfanatics.net/uploads2/rbe2-aztecs-150bc.zip