Atlanta and New Orleans in the West bothers me (Just like it does in the NBA), need to come up with names for conferences that aren't geographic in nature if you're gonna go this route IMO.
The NFC before 2001 (and the 8x4 alignment) must have driven you insane.

I put ATL and NO in the NFC West because that was historically their home. Same reason I wanted to put Tampa Bay in the NFC Central -- that was where they resided back in the day.
I could see a variation for the NFC of...
E = DAL NYG PHI TB TOR WAS
C = ATL CAR CHI DET GB MIN
W = AZ LAR NO SF SEA STL
Move TB to the NFC East -- the large fanbases of the other teams in the division would appreciate a winter vacation to Tampa and/or already live down there. Tampa has a ton of snowbirds. I would imagine TB would sell a lot of tickets to retired Giants, Eagles, Washington, and Toronto fans.
ATL and CAR moved to the NFC Central as the best geographical fits.
NO and the STL expansion are somewhat "western" teams. The St. Louis Rams were in the NFC West before moving back to Los Angeles. NO is the most isolated of the NFC South teams as it is. So send them out west with the four West Coast franchises and maybe that solves some of the problems you had.
I think the important part is keeping the NFC East and NFC North as they are now together, which this does.