I see it working out like this:
Rice beats Tulane, wins the West outright.
Rice goes to C-USA Championship vs. ECU, ECU wins.
ECU goes to Libery Bowl.
Rice goes to Hawaii Bowl.
Then it becomes a hot mess. Tulane, Marshall, MTSU, and North Texas need to go somewhere. (Assuming UTSA gets left out).
Best geographic fit:
Heart of Dallas - Tulane or North Texas
Military Bowl - MTSU or Marshall
Beef O'Brady's Bowl - Tulane or Marshall
New Orleans Bowl - Tulane, MTSU, or North Texas
If you go strictly by conference ranking (today):
Heart of Dallas - Marshall
Military Bowl - Tulane
Beef O' Brady's Bowl - North Texas
New Orleans Bowl - MTSU
Note - Heart of Dallas did select Houston in 2012 even though Houston was the #1 team out of C-USA