I'd go with 17 teams (hear me out)...
The top 15 are automatically in..., with numbers 16 and 17 matching up at a fixed neutral indoor site (I nominate Lucas Oil Stadium) in a Thursday night play-in game for the right to be the 16th team in the playoff... Byes to be determined by final Sunday before the play-in game rankings only, no other considerations may apply...
That gives the top 17 a more than fair shot to be in it and if you can't break the top 17 by end of season there really shouldn't be any valid argument about why a team should have made it; they'll have had 12 regular season games, possibly a conference championship game, and if they're #17, a play-in game, to make their case...
This format would be a $$$ maker too which is all the networks and the conferences actually care about... It would also get 5 more fan bases involved and (in theory) open things up to possibly one or two schools who would rarely have a shot at the current 12 team setup...
You could keep the Home game for the first 4 games (not including the play-in) and then attempt to go with indoor pro sites, my cedar with fair weather former Bowl sited from that point on asassigned by a closest to the highest ranked team criteria (someone's not gonna get a fair shake there but there are only so many venues available)...
If you go by the Sunday rankings after the last conference championship game then those championship games would still have real meaning (even in terms of playoff sites assigned...)...
Now I'm certain there are flaws in the above format but I doubt they insurmountable...
If that had been the format used this season BYU and Clemson would have faced each other in the play-in game and Alabama, Miami, Ol' Miss and South Carolina all would have made the Playoffs...
The really big payoff: No more having to hear all the whining from Herbstriet and Kiffen...