i have been mostly following
this guide. only difference is that this guide says you need to talk to every single villager every time in order to prompt them to have a thought bubble - this is not true. i'll just TT, run around town and see if anyone wants to move out, and if they don't then i TT again. the villagers you want to move out will ask eventually, but it might take quite a while, as the other 5 will also ask.
if you really want those villagers gone, i would recommend just going ahead and doing it. there's no punishments for TTing other than your turnips will spoil if you haven't sold them yet, and weeds will grow. i just TT to cycle out the villager and then come back to real time once they've asked to move out.
edit: and let me know if you have any other more specific questions - i'm not an expert but i've cycled out four villagers so far and feel like i have a handle on it.