IF the Jaguars were to move to LA, then I could see a change of divisions - but not to the AFC West. Those four teams have rivalries going back to 1960, I can't see any of those four teams agreeing to such a change, especially considering that none of them would be changing locations.
My first thought would be to swap with the Rams since they are the only other team in a West division that is in the central time zone. The only potential hurdle I can think of is if the networks don't like having those two midwestern teams from Missouri (Chiefs and Rams) in the same conference, but it makes the most sense. You know Dallas isn't going to move from the NFC East, you don't want to break up the NFC North for the same reason you don't want to break up the AFC West, and swapping with New Orleans doesn't make sense since all the other NFC South teams are on the east coast.
However, lots of teams have been rumored to move to LA, including San Diego, Minnesota and St. Louis. At this point I'll believe it when I see it.