If the issue is mostly the timing of characters actually physically entering into the game, what if you altered the app process so that apps can be submitted during a certain period (like maybe even the last week of the month) but aren't processed/ or even looked at by you even until the beginning of the month? A lot of the "rush" comes from when people see "hey there's an app for this canon I like maybe I should app a canonmate". If you could submit apps for a longer period you'd have time to look over what's been submitted and write your own, but it'd still keep the intros at the beginning of the month so they wouldn't interfere with plotting. And if you indicate that you're only even going to start looking at the apps at X date it won't give you extra modwork either.
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