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Ack. I did up the 1962 & 1963 seasons. Even automating the process somewhat it was still quite tedious. I could probably automate it a bit further, but I would not relish the idea of trying to do the whole MLB list.
Mostly I moved the "extra" games to days where both the teams were off, and in most of those cases I was able to keep those games contiguous with other games those teams played. There were cases though when there was no choice but to drop the moved games as 1-game series, but I at least tried to keep the travel considerations at realistic as possible in such situations.
For 1962 I found enough regular offdays through the already set regular season length in which to put the games. However, this required wiping out the brief break for the 2nd All-Star Game of that season (7/30-7/31), and that season was a week shorter than the seasons these days, so teams have ~7 fewer offdays than now and long stretches of days playing in a row, a few around and even over 2 months. For 1963 I tacked on a couple extra days to the season for many of the teams and the consecutive days playing streaks, while still quite long, are not as long as for 1962.
I do not know that it would be appropriate to post these editted versions here in this thread. Maybe I will put them in the fictional schedules thread.
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