Say it with me: league associations... you want to see league associations implemented.
With that, you'd just create as many separate leagues as you want in your universe. If you want to have some of them grouped together, you put them into an association which allows certain kinds of interaction between those leagues. Subleagues would remain, but renamed conferences and used within a league for setting up conference structures such as that used by the NBA, NFL, and NHL.
As for your 1961 scenario. there is the question of how the World Series would have worked with three leagues. The idea of a wild card qualifier had not really been invented yet, and would have been anathema to the major league owners at that time even if it had. So you'd be left with three league winners but only two World Series berths. There was a proposal by Branch Rickey that would have involved a three-way World Series. I think I have onhand the TSN article where the idea was suggested...