I don’t think I can manage the stress of a game of diplomacy. Well, unless it were no press.
Back on the subject of Republic of Rome, I think it would be pretty much ideal as a moderated forum game. The game is extremely structured in most phases, so the moderator can control all the procedural elements.
The obvious difficulty is in the timing of tribunes and particularly of assassination attempts.
Tribunes are on a first to shout basis, which could be modified to a randomisation between people wanting to play them at the same point in the process. With them generally playable at any point during the previous motion, there should be plenty of time for everyone to choose.
Assassinations are designed to be interjected at specific moments in the procedure: eliminating a key source of opposing votes just as they are called to vote but before they can cast their vote, for instance. Happily assassinations aren’t all that common, in my experience. I think we’d just need to allow a little flexibility here and it should work smoothly enough.