I recently managed total domination on an Expert campaign as the Byzantines by 1225. At endgame I had 2 full stacks of Varangian guard and 2 stacks of Kataphraktoi sitting unused as reserves in Constantinople (as well as stacks of Pronoiai, Lancers, Byz Cav, Treb Archers, Byz Inf, and Spearmen), so I imagine I could have accelerated my time if I'd focused on it. My goal was to dominate before the Horde arrived, which I achieved. I get a kick out of building up infrastructures, so I tend to focus on that more than racing to victory. It's fun to have a buttload of really nice troops just kickin' it in the capital, partying and waiting for the call to battle. I get a kick out of seeing them all there. 1166 is damn fast though ... I'll have to see how hard it is to match that.

My standard Byz army stack tends to be something like this (which would not be the case if I were to play MP ...):

40 Kat or Pronoiai (Command)
80 Lancers or Pronoiai
80 Byz Cav or Steppe Heavy Cav (Horse Archers early on)
180 V.Guards
200 Byz Inf
200 Spearmen
180 Treb Archers

When I can I'll hire Italian Light Inf, Feud/Chiv Sergeants, or Order Foot to replace spearmen. Pronoiai are built in Nicacea, Treb Archers in Trebizond, Kats in Constantinople, exclusively for the most part, for +1 valor. I try to have two provinces constantly producing VG, as soon as possible. Simply put, they ROCK.