Apologies, guys. Have been putting in 90+ hour weeks at work, looks like I screwed up the example team after the second player (never do anything in 20 minutes that deserves longer).
The TLDR for this theme is as follows: I start the chain with 1887 John Kerins, who played for the Louisville Colonels. I take one other player who played for the 1887 Louisville Colonels (Elton Chamberlain), and twist them to another season of their career (in this case 1888). I then use that season, 1888 Elton Chamberlain of the St. Louis Browns, and twist a member of the 1888 St. Louis Browns, and repeat this process until I have 25 players.
Unfortunately, in my example, I used Lave Cross, who did not play on the 1888 St. Louis Browns but instead played with Elton Chamberlain in 1891, when they were both members of the Philadephia Athletics, and then proceeded in that fashion instead. This is incorrect. I am deleting the example team to avoid any, rightful, further confusion and will post a (correct) example later today.