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I took a couple different approaches below, similar to as discussed but different in various details. For each league configuration there is one case of having very regular offdays but not quite as frequently as you were wanting and one case with more offdays though a few instances with slightly longer streaks without an offday. These allowed for keeping the "baseball week" in order and making so all teams have the same number of weekend games.
I cannot speak to the game's handling of doubleheaders. I tend to avoid using them unless requested because they are uncommon these days. Setting them is also more effort in my process.
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