a conference game. A conference has the freedom to write its own rules. I am saying that all 12 AAC members would play 8 conference games. It just happens 1 conference game would be played after the Conference Championship Game was played. The reason I say that the AAC would count the Army-Navy Game in the conference standings, but the game wouldn't count towards determining Army's and Navy's eligibility towards playing in the Conference Championship Game is because AAC has to comply with another NCAA bylaw in order to even be able to host a Conference Championship Game.

17.10.5.2 Annual Exemptions. [FBS/FCS]
17.10.5.2.1 Bowl Subdivision. [FBS] In bowl subdivision football, the maximum number of football contests shall exclude the following: (Revised: 1/10/90, 11/1/07 effective 8/1/08, 10/28/10, 10/27/11 effective 4/1/12, Adopted: 8/2/12 effective 8/1/14, 1/15/16 effective 8/1/16)

(b) Conference Championship Game. One conference championship game:
(1) Between division champions of a conference that is divided into two divisions (as equally balanced in number as possible) and conducts round-robin, regular-season competition in each division; or
(2) Between the top two teams in the conference standings following full round-robin regular-season competition among all members of the conference.

A 12 team can't satisfy #2 unless the conference is willing to play 11 conference games. Even then by your logic the AAC would be in violation because the Army-Navy Game wouldn't count as a conference game even if it was a conference game (chew on that idea for a little bit) because the game was played after the AAC Championship Game was. Hence why I said the AAC would count it in the standings and comply with this bylaw, but not count it towards CCG eligibility.

So if the AAC wants to host a CCG, then it has to satisfy #1. If Army and Navy are placed in the same division, then the AAC would have to count the Army-Navy Game as a conference game in the standings, even though it was played after the CCG or else be in violation of #1 because of the round robin requirement. Basically the NCAA would not allow the AAC to count the Army-Navy Game as satisfying the round robin requirement if the AAC doesn't count it as a conference game.

Essentially Army and Navy would have 7 conference games count towards CCG eligibility while the rest of the conference would have 8 conference games. It would place Army and Navy at a disadvantage when it comes to tiebreakers, but that would be the choice the 2 schools would have to make to keep the Army-Navy Game on its current date.

No, Army is still a DI-FBS Independent. The reason I mentioned Army is because the AAC kicked UConn out of the conference in all sports when UConn decided to return the Big East. As a result, the AAC currently has 11 teams, plans to keep the 2 divisions, keep its current 8 game schedule, and still play the AAC Championship Game at the end of the season. If Army was willing to join the AAC as a football-only member, then the AAC would have 12 football members again. Also, the AAC would have exclusive rights to the Army-Navy Game plus two-thirds of the Commander-in-Chief's Trophy games with the MWC retaining Air Force's rights. A 12-team conference makes it easier for scheduling purposes because an 11-team conference will probably end up violating the round robin requirement for divisional games. FWIW when the MAC had 13 members, it violated that bylaw because 1 division with 7 teams and 1 division with 6 teams couldn't play a round robin divisional schedule and still play a total of 8 conference games. The math doesn't work even if the MAC had switched to a 9 or 10 game schedule.