With how often title games since the dawn of the Bowl Coalition era in 1992 have matched two Southern teams, I think it would be better if the 12-team CFP is divided along the Mason-Dixon line, with the top 6 teams from outside the South as defined by the US Census Bureau competing for one bid in the title game, and the top 6 teams from the South as defined by the USCB competing for the other.
The highest ranked G5 champion would take the place of what would be the sixth-ranked team in one of the regions if they are ranked low enough in the final CFP rankings. If the G5 team is from the MAC, MW, or is Army, New Mexico State or Temple they would be in the part of the bracket with teams from outside the South. If the G5 team is anyone else they would be with the other teams from the South. If the G5 champion happens to be one of the top 6 from one of the regions, then they would not replace another team.
This format allows teams in conferences who didn't win their conference as well as independent Notre Dame to earn first-round byes, something which would be prohibited under the other format being proposed.