So, I've skipped Fishing, here. I want HBR sooner than later and don't need the food.
Eastern gold city comes 4th because it instantly borrows the corn from the capital and, hence, slows down settler/worker production.
5th city is planned to claim the western horses, probably on the plains hills.
Huuuum... So, Shaka started plotting as soon as I planted Tlatelolco, which is kind of expected and the not wise part. You might prefer to delay that city for safety. This is why I'm on the archery path atm.
At least, I've got all the food in sight, which is, you know, the objective in early expansion. Also got decent prospects for the capital's cottages development.
Triggering the DoW is really bad, actually and I'll probably die in the next 20 turns or so

But my issue with your attempt is that your first 2 cities do not claim tiles (other than a gold tile, which... does that really count ?). I think a middle ground can be reached that could both be reasonable and efficient.