Army-Navy will be game of the century.
The crazy thing is Army has joined the AAC (which Navy was already in). They decided to keep the Army/Navy game as non-conference game taking place after the season is technically 'over'.
So Conference championship weekend is the week BEFORE the Army/Navy game.
They could actually play each other back to back weeks.
Friday, December 6th. AAC championship game
Saturday December 14th. Army/Navy game.
Remaining conference games
Army: North Texas(5-1/2-0), UTSA (3-4/1-2)
Navy: Rice(2-5/1-3), South Florida(2-4/0-2), Tulane(5-2/3-0), East Carolina(3-4/1-2)
Both Army and Navy have regular season games against Notre Dame, but those obviously aren't conference games.
BTW, the bowls and playoff selection is done before the Army/Navy game so it won't have any impact on them. The CFP/bowl selection happens on Sunday December 8th. Although it could happen following their 'first match-up' in an AAC championship game. The second army/navy game would not have any impact.