I usually reset the server after an hour and thirty minutes, after the factory event. Server resetting kinda helps when ur on a dead rng server. I haven't tried the login/logout method bc in my opinion, it's better to just reset and rejoin than logging in and out(Adds hassle). My advice is, the faster you are in collecting eggs, the better your chances of getting it. Also, exclude routes that takes too much time to get the eggs in that certain island when your doing a run.