The GP's example doesn't involve invalid datetimes. The datetimes aren't out of bounds or invalid in any way that a check constraint would detect. They've just become factually incorrect ("bad data"), because they are derived data that wasn't updated when the derivation rules changed (i.e., regulatory changes).
If you're storing future datetimes that semantically represent wall clock time, you need to store the locale time plus the full time zone (such as America/New_York) so that your program does the right thing in response to any common regulatory changes that happen after you store the value. Storing the time zone abbreviation (e.g., EST) is inadvisable, as computers sometimes care whether you asked for EST vs EDT. Storing the time offset (e.g., -500) is incorrect, as it has the same pitfalls as storing UTC - you're precomputing the locale's expected time offset at storage time, and your data won't automatically be corrected if time regulations change.
If you're storing historical timestamps, UTC is fine because you can safely convert it to whatever time zone you want to display, knowing that changes to time zone / DST regulations tend not to affect the past.