If you're feeling nice, randomize whose time remains stable (to keep things fair), keep the organizer's time stable, or pick the time that minimizes the number of participants who will have the meeting time change.

If you're feeling mean, randomize whose time remains stable (to make it hard to predict), move the meeting for the organizer, pick the time that maximizes the number of participants who will have the meeting time change, or split the difference and move everyone. Meeting was at 10 AM for Alice and 9 AM for Bob, but now it can be at either 11 AM for Alice and 9 AM for Bob or 10 AM for Alice and 8 AM for Bob? Now the meeting is at 10:30 AM for Alice and 8:30 AM for Bob.

This is the critical problem with all of this.

Daylight savings time changes, can't be globally banned fast enough really.

Every event should have an IANA timezone tied to a city like America/Vancouver or Europe/Berlin, and it should ideally be settable by the user. Some apps (e.g. Discord) don't expose this but have a time zone under the hood, and it's a huge pain every time daylight savings time comes along when an event's time zone is incorrectly in Europe instead of North America