I am going to be moving next year and had much the same thought about using it as a chance for a new start, out in the open. I think it's a great idea.
As for talking to your parents, while you may worry that during something like this would be a bad time, the truth is I'm not sure there ever is a "good" time. I mean, obviously you don't turn to your left during a funeral and say "Oh, by the way, I'm transgender.", but pretty much aside from any extreme examples the time that is right is the time that works for you, regardless of other circumstances. When I came out to my father and then step mother, they were both very busy and stressed dealing with some major work stuff. But I also knew that even if I waited for that to be resolved, there would be something else. Then something else. Then something else again. That's just how life goes. The odds of finding that one, perfectly empty, not stressful moment that also aligns with your desire to come out is slim to none.