Wow, great list indeed CBBL. I also use this site for defunct leagues and teams to help spark ideas:
http://www.ballparkwatch.com/league_histories.htm
I know 1833 is a bit odd. I started my league in 1800. I imagined an organized town ball league that morphed into a major league. My major league is called the American Town Ball Association.
Twenty years later, I added an International-level league over in England. For that, I imagined a popular combination of Rounders and Crickets catching on to form a game that resembles our baseball. The league I have in England is called the BRACA, or British Rounders and Cricket Association.
Now, looking over those players left in the draft pool, is why I want to start a Class A league.
I will probably start the Southern Association after the Civil War. In history, it started in 1885, but I likely won't wait that long.