I actually got this to work, and it was really pretty fun. It beats the monotony of a generic spring training. My team got to play other major league teams from the other league (I don't have interleague play), as well as teams from Europe, South America, and Japan.
First thing I did was calculate it would take six weeks to run a tournament of this type: with five 10-team pools, each team would play two games against each team in their pool: 18 round-robin games, plus three rounds of playoffs (the five pool winners, plus three wild cards). So I had to start the tournament the first week of March. Also:
- I shortened spring training from the default five weeks to two weeks. Spring Training started literally the day after the tournament started, so I will have to watch this going forward, because I don't want a team playing a tournament championship and a spring training game on the same day.
- I then moved my regular season from the first week of April to the first week of May.
I did forget to adjust the regular season start dates of the Europe, Asia, and South American Leagues, but none of their teams made the playoffs, so it didn't matter much. But I would need to fix this going forward, because one of their teams might make it to the playoffs some day.