Leave before June.
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Not necessarily. I don’t think the time has to be consecutive days. You can come and go as long as your total time of residency in your new state (i.e., be present there) is at least 184 days.
For those who are interested, there are multiple iPhone & Android apps that help prove 'non-residency' by recording GPS localization on a daily (or better) basis. As well the app(s) frequently help in establishing the various legal proofs needed to show changed residency.
FYI though, there is a history of the states trying to continue taxation of pensions earned within and while a state resident. While this was killed decades ago by a US Supreme Court decision, I can see it coming back by a US Congress law.