I'm currently in the process of advancing this dynasty to 1876. For those of you following along with the process of this fictorical replication and not just the results, here's a summary of where I'm at.
There were 6 teams from the NA that helped form the National League in 1876. Two additional teams that were not part of the NA rounded out the initial 8 teams. In order to keep the team records separate, I did not want to move the teams from the NA to the NL. For that reason, I added a new major league called the National League. I wanted the NL to have players from the NA in it, so I declined the option for an inaugural draft when creating the NL. The game then created the teams and filled them with players. The next step is to clear out those rosters. You have to release all the players, then delete them in the Free Agents screen. You can't just delete them directly from each team's roster.
Next, I'm moving the players one-by-one from their NA team to the correct NL team. I'm doing this by going into the player editor and reassigning them to the new team. The final step is then to delete the NA league. At this point, the existing NA teams that weren't part of the NL still have all their players on their roster. For me, that was fine, as deleting the league just releases all those players into the free agent pool. The league history of the NA still shows up on the history pages, and the players still have their NA stats credited to them, but the league is gone.
I still have some player moves left to do, and I'm in the process of creating an 1876-1900 FaceGen pack for use with this league, as I wasn't able to find anything like that. There's little documentation available in terms of what team logos and jerseys looked like in this era, so where I haven't been able to find it, I'm just making something up. I'll release it all to the OOTP community when done. Anyway, that's where I'm at.