I know this is an old thread but...
I'm surprised that no mention has been made of the hippodrome, which is surprisingly good for attempting cultural victories in the late game.
This is counter intuitive I know, because the UB doesn't allow you to select artists. But, setting the culture slider to 30% will give you another six happy, you're bound to have horses and the hippodrome without modifiers should give you another 3 smiley faces in your cities. More than enough to manage caste system even when other civs have adopted emancipation: which provides unlimited artists. Put it up to 100% for the final push and unhappiness from any source isn't even going to be an issue.
I'd play with justinian a little differently from the way the outline in this article goes. Your main benefit in the first 50 turns is going to be the ability to expand and this requires hammers, so I'd focus on techs to develop the land first, building a worker straight off and actually not worry about going for an early religion at all.
I'd then use the oracle to acquire code of laws, and the great priest from this to acquire theology. If any neighbours have spread an early religion to you, there's no reason why you can't adopt this if it benefits you diplomatically, but make sure you switch back to your relgion before finishing the AP, swopping back painlessly due to the spiritual trait to maintain relations.
The cheap temples would then make it easier to use the hammers bonus you get from religious buildings to give you a manufacturing edge. I'd spread my religion frugally to those I wanted to befriend, and use this to isolate opponents (spreading your religion to theocracies is not impossible: gift them your missionaries and because it's the AP religion they'll spread it for you). I'd top this off with acquiring university of sangkore and spiral minaret. Even if I don't choose to stay as my religion, temples of any religion are easy enough to build or whip.
Finally, the sistine chapel provides a signficant culture boost to state religious buildings, so if you have marble, go for music sooner rather than later. Cathedrals are an integral part of going for a cultural victory and whether or not you choose confuscianism or christianity as the ap religion will be heavily dependant upon whether you have bronze (a boost to building confuscian cathedrals if I remember correctly) or stone (a boost to building christian cathedrals).
And don't forget, if you have the AP and no-one has adopted your religion, you're the only one eligible for a diplomatic victory.
As such, I'd question the assertion that Justinian is only a warmonger because of his traits and UU. The cataphract because of its comparative strength isn't something I'd make a point of b-lining as it remains relevant on the battlefield far longer than the praetorian (it's nearest UU equivalent because of its strength bonus). I'd think of him as more of a balanced leader, capable of succeding either militiaristically or peacefully.