As far as I’m aware, GMT has never changed since the advent of computing.
Yes, you do need to store the location of the scheduler so that you can adjust everything as appropriate, and of course you need to schedule the time the event was created. But you still only store those times in GMT.
By the way, what I’m describing is the way every AWS system does it.
Edit : Oddly, I can’t reply to your reply to this, but I already addressed the case you were talking about in this comment.