So i read on here somewhere that becoming best friends with a villager you want to leave will help them move out faster then ignoring them. So i've been sending the villagers i want to leave letters but it doesn't seem like its working. I do other things besides writing letters but i was wondering if writing letters might make them stay instead of leave?

I don't like ignoring my villagers because if they ping me it might be for a PWP or something else instead of leaving and then i feel that puts me behind on progress of them leaving.

All you can do really is just wait for them to leave. There are tons of theories and some work and others don't. Just wait for a villager of yours to talk about them moving so that way if the villager you want to move tells you they are moving, there won't be a chance that they will change their mind.