I swapped Winnipeg for Calgary, which makes for 12 teams west of Texas. Only Arizona and Denver aren't in the West Divisions:

AFC East: New England, NY Jets, Buffalo, Baltimore, Indianapolis
AFC South: Miami, Jacksonville, Tennessee, Houston, San Antonio*
AFC North: Pittsburgh, Cleveland, Cincinnati, Kansas City, Denver
AFC West: Calgary*, Edmonton*, Las Vegas, LA Chargers, San Diego*

NFC East: NY Giants, Dallas, Philadelphia, Washington, Toronto*
NFC South: Tampa Bay, Arizona, New Orleans, Carolina, Atlanta
NFC North: Green Bay, Chicago, Minnesota, Detroit, Saint Louis*
NFC West: Vancouver*, Seattle, Portland*, LA Rams, San Francisco

Schedule would be 8 games against your division rivals; 5 games against 1 division from your own conference; and 1 from each of the divisions in the opposite conference (based on order of finish)

Twelve teams in each conference make the playoffs, but all of the division champions get byes. This leads the NFL to have a Friday Night and Monday night playoff game in both the Wildcard and Divisional rounds:

Friday 8:00 PM Eastern
Saturday 1:00 PM Eastern
Saturday 4:40 PM Eastern
Saturday 8:20 PM Eastern
Sunday 1:00 PM Eastern
Sunday 4:40 PM Eastern
Sunday 8:20 PM Eastern
Monday 8:00 PM Eastern

Based on this season's calendar, this would be:
January 21-24, 2022: Wild Card Round
January 28-31, 2022: Divisional Round
February 6-7, 2022: Conference Semifinals
February 14, 2022: Conference Finals
February 28, 2022: Super Bowl

The College Football Playoff responds by moving its championship game to Thursday night.