Alex Vance
Basil II's Junior Emperor
Just go for a warrior/archer rush with battering ram support, and upgrade those warriors into swordsmen as soon as you can.
With Crusade you are well positioned to knock down a neighbouring deity AI (in fact its my go-go rush), and with Taxis and early political philosophy for Oligarchy you are more than well equipped to knock the neighbour down.
Sure you lack the speed of cavalry units, but early on battering rams are good enough provided you have Crusade in place.
The trick is to spend the first faith on a missionary to convert the closest city before you declare war, and then just steamroll from there.
Unlike other civs that might struggle to convert while at war, city conversion is essentially free and unavoidable from that point on for Byzantium.
Listen, I'm just going to be honest about this: you're one of my favorite posters here. I generally agree with what you say.
On this aspect, however, we'll have to agree to disagree.
Tagmata are, in my experience, an extremely powerful UU; and PotatoMcWhiskey recently speculated that Tagmata may be the strongest UU in the entire game. (I personally disagree, but I do think they're in the top 5.)
Having a Knight that's also a mini-Great General that all buff each other (on top of normal combat unit proximity bonuses) -- and don't require Science, which you should have zero interest in as Byzantium (as they obtain Science indirectly by conquering cities with Science-producing buildings)? Sign me up please.
The fact that they also affect Missionaries and especially Apostles adds an element of versatility to them, as well.