Hi, thanks for your post. This is a pretty sophisticated question for a “WP novice”, so it sounds like you are doing great.
Schools was created for sites not unlike your own. They came about primarily so you don’t have to enter all the data like mascots, logos, etc for all the teams in the same school. And the “School Sports” metabox allowed one site to display the schools teams/sports on each school’s page, but that requires custom coding in that theme.
As far as adding teams to leagues, I’m not quite sure what’s going on with WP Import/Export, but here’s some sexy WordPress stuff that could be a hint. The leagues for a team is not a properties (data elements) of the mstw_lm_team custom post type. A league (mstw_lm_league) is a taxonomy (custom category or tag if you will) into which a team can be placed. (You can actually determine that from the Edit Team admin page). That allows each team to be placed into multiple leagues easily, e.g., the 49ers are in the NFL, the NFC, and the NFC West. That may or may not be the best design, but it was done many years ago, so we will have to live with it.
Let me know.
-Mark