I've also thought about Spring Break but something about the timescale the more I look at them feels like there'd need to be sudden weeks skipped and it feels increasingly like that ship has sailed given where the story's going.Not really. We already know episode 11 will take at least about another month to around Christmas, so it might be that (unless episode 12 is almost completely about New Year) S4 might end on or just before Valentines. We also know that DPC says he needs at least to episode 14 excluding epilogues for the main story. My guess (and many others) is rather that the complete BaDIK ends around Spring Break than Valentines.
I struggle to see S3 itself ending post-Christmas at this point, especially given the teaser at the start of S3.