Copied and pasted from an answer that I gave to someone that was asking the same questions:
"As far as game mechanics go... Advancing your game by more than a day increases the internal (days played) clock by 1. So increasing it by a month is only going to give you weeds, no extra fossils or gyroids. A villager might move but never more than one and if you were advancing by 2 days per trip would have achieved a similar result(except they usually ask instead of disappear). Also if you don't talk to a villager at all, they tend to be more stubborn about moving. You can also use the PW trick to make them ping you and sometimes that triggers a move conversation. (public works trick being: grab a swimsuit, swim out of reach for 5 minutes, fill all your items with things like bells and tools, swim back and stealthily target the villager you want to ping usually the first one will ping you unless you have a you've been playing too long thing going. If that is the case, talk to one you didn't want to ping, so he can clear the conversation. The next person you run into will ping you for a conversation. If you have items that cant be bought or traded it reduces the conversations they can have with you raising your chances of having a PW or move conversation)"