First, get rid of conference divisions and championship games. Reorganize the P5 Conferences into:

Big Ten:
Ohio State
Penn State
Michigan
Michigan State
Wisconsin
Iowa
Notre Dame
Texas
Oklahoma
Nebraska

SEC:
Florida
Tennessee
Georgia
South Carolina
Alabama
Auburn
LSU
Ole Miss
Mississippi State
Texas A&M

ACC:
Clemson
Florida State
Virginia Tech
North Carolina
Duke
Miami
Louisville
Georgia Tech
Pittsburgh
West Virginia

PAC-12
Washington
Washington State
Stanford
Oregon
Colorado
USC
Utah
Arizona State
UCLA
Oklahoma State

Each P4 conference has 10 teams. Each team will play each conference team once (9 games). They will then play 3 Conference Challenge games (12 total games).

Conference titles account for just that: conference titles. The Committee rankings will then determine who plays who in the "Conference Challenges". Conference champs don't automatically get to play conference champs because say for example Penn State and Ohio State both go 11-1. Penn State has the head to head over Ohio State early in the season, but then loses by 30 to Michigan State in the last game of the year. Most likely, Ohio State would end up ranked higher.

Committee procedure:
The Committee will rank all 40 teams from the P4 conferences. Then, for 3 weeks, each team will play in a conference challenge against their rankings equal (ex: the 4th highest ranked B1G team will play the 4th highest ranked PAC team). CONFERENCE STANDINGS DO NOT DETERMINE. COMMITTEE RANKINGS DO. However, Conference Standings will be taken into account when ranking. The Rankings will change weekly.

Week 10: Big Ten v PAC 12, ACC v SEC
Week 11: Big Ten v SEC, PAC 12 v ACC
Week 12: Big Ten v ACC, SEC v PAC 12

After week 12, the Committee will release their rankings for the College Football Playoff. Regardless of conference, the Top 4 teams will play. If the Committee believes the top 4 teams are from one conference, those top 4 teams will play.

Example:
Although it isn't perfect since these CFP rankings take into account an OOC schedule, the theoretical conference challenges would look like:

B1G #1 v PAC #1: Ohio State v Washington
ACC #1 v SEC #1: Clemson v Alabama
B1G #2 v PAC #2: Michigan v Colorado
ACC #2 v SEC #2: Florida State v Auburn
(and so on)

So then, say for week 11, the new rankings come out. Ohio St, Alabama, Colorado, and FSU win (this is just a few of the games. There will be 20 games each week).

Big Ten v ACC #1: Ohio State v Clemson
PAC 12 v SEC #1: Colorado v Alabama
Big Ten v ACC #2: Wisconsin v Florida State
Pac 12 v SEC #2: Washington v Florida
Big Ten v ACC #3: Penn State v Louisville
PAC 12 v SEC #3: USC v LSU
(and so on)

Say for week 12, Ohio State, Alabama, Florida State, Penn State, USC, and Florida win

Big Ten v SEC #1: Ohio State v Alabama
ACC v PAC-12 #1: Florida State v USC
Big Ten v SEC #2: Penn State v Florida
ACC v PAC 12 #2: Clemson v Colorado
(and so on)

Say Ohio State, USC, Penn State, and Clemson win. Projected Top 4:

Ohio State
Alabama
USC
Penn State

Final:
12-14 game season
10 team conferences
9 game regular season (conference)
3 Conference challenge games
4 team playoff