Here’s the solution, assuming a four-team playoff:
Have all of the traditional bowl games on New Years’ Day.
The National Semifinals on Jan 2.
The National Championship game on Jan 9.
I have suggested something similar to what you have suggested. Instead of the BCS picking two teams they should pick 4 teams and play a two semifinal games on New Years Day and then maybe a week later play the championship game.
2012 to 2015:
Four-team playoff with two current BCS bowl games for semifinals on New Year's Day and final one week later.
2016 and beyond:
Eight-team playoff with #1 versus #8, #2 versus #7, #3 versus #6 and #4 versus #5, quarterfinals played first weekend in December at home stadium of higher-ranked team. Reseed four remaining teams and play semifinal and finals using method I mentioned earlier.
You do know that several years ago (the year an undefeated Auburn got locked out of the BCS championship game), the SEC pushed hard for exactly that: a 4 team playoff.
Every other conference except the SEC turned it down flat.