You actually CAN edit conferences & what team is in which conference by editing the Teams.xml file, however you need to make sure that the "LastYearStandings" field does not have duplicates. What I mean by this is that the "LastYearStandings" of all teams in the conference should be sequential. You cannot have duplicate standing positions. This will crash the game.
I've done the following and it DOES work:
1. Swapped teams in different conferences by keeping the IDs the same and swapping the other values
2. Fixed the LastYearStandings values.
Here is the edited Teams.xml
https://pastebin.com/raw/xNKkdaiT