Interesting stuff guys, as I too am trying to figure out how I'm going to get all these up to past 80 (FYI, as I'm sure you've seen, the moments and things don't unlock for Stage 2 until 80 for some reason). I've got 3 teams at 100 percent, another at 95 and that's it for unlocking through FOTF. I'm getting close on Yankees.
I was having issues with Stage 1 showdown, so I was doing MTO. FWIW, it seems like MTO runs are taking longer these days (and worth fewer affinity points). I was playing Yankees today and I haven't lost a single "moment" yet on my MTO run, but it's taking quite a while. I'm still not to the All-Star break yet. I haven't accepted any trades (which sometimes take longer because you have to play with that player for a game and I have baserunning and fielding shutout in player-lock moments). But I played for a few hours today and still didn't make the All-Star break yet, my second time playing this current run.
Good tip from @bonion. Maybe it's best to do the Stage 1 Central showdowns, since they are a bit easier and save the exchanges for the other divisions. I might try that approach, though I'm not a big fan of exchanges in general.