A stronger Persia with more of a dislike for Greece would definitely help, as in most games I have seen, Greece get's strong enough to block Rome's eastern expansion. The biggest problem though is the AI's inability to mount a naval invasion. There has to be something that forces Rome to cross the Mediterranean. Phoenician cities could be the key if Rome was set to Total war against them. Maybe against Persia too.
The other issue is production and timeline. There is just not enough production capability in the time frame needed to create enough troops, move the troops and do the conquering, while still building the required buildings and fending of the barbs. Maybe the civ's UP needs to be change to give this a hand. Something like the conquerors event, where you receive an army whenever you conquer a city in a new continent. The use of romanized local troops was key to rome's empire. Or maybe the building UHV condition could get changed to something not production oriented so all of Rome's production could be building Legions. Making Rome OP is not that bad cuz Rome frickin was OP!! As long as it is controlled with stability and civ spawns so that it is temporary, it shouldn't really effect the full game.
Also, what he said ^^^^^^
Also, is their any way to make it so a UHV is counted and acknowledged, but it doesn't actually create a victory? I would like to, for instance, win a UHV with say Rome, but then keep playing and switch to another civ when it spawns. I know you can keep playing, but civ switching, other victories etc are disabled. For some reason I think it would be kind of neat to travel through history like this and create alternate worlds. It'd be fun to play in a map that was a legacy of your earlier triumph.