The aforementioned third group could easily be the Freemasons. Everyone seems to think they're this powerful entity that secretly controls things, but no one actually has a clue what, specifically, they do. Having them be the one behind the scenes working very hard to prevent interesting things from happening seems like a perfect fit. As an added bonus, a lot of historical figures from the American Revolution either were or are suspected to have been associated with them, so this game would have been a perfect opportunity to introduce them ... and introducing them would have been a decent excuse to set the game during the American Revolution.
I mean, really, National Treasure was a cheap attempt to cash in on The Da Vinci Code's popularity, and even it had a better excuse to be about the Founding Fathers because of the connection to a real secret society that was around back then. (Hell, there was probably more historical fact in that movie than The Da Vinci Code itself, not that that's saying much.) The Knights Templar got a mention in the movie, but unless I'm mistaken, they were assumed to have been long gone by that point.