I have a pretty good method to time traveling that seems to always work great for me so I guess I'll share haha. After someone moves out, don't time travel forward any further than five days. Then after that, you use the same method that you use to cheat and get public works projects. Go day by day. Empty your pockets of money and everything and put on your wet suit and swim out to the rope in the beach water. Sit there and get stung by jellyfish for five or six minutes and then get out and a villager will ping you. You may have to do it up to five or six times but if someone's gonna move, they always tell me when I do that. It takes a little longer but its pretty much fool proof