Hi: From my own experiences, there are a numbers of ways to trigger them to move / avoiding them to become one of those dreadful 'anchor' villagers.
Sad, sad disclaimer: I have one very determined O'Hare who anchored himself in Tamago.
(my oldest cycling town from 1.5 years ago)
HE IS STILL THERE. So I totally feel your frustrating with Stitches.
Have you tried drastically changing the cycling month/season?
- when 'looping' within a set of cycling days (i.e. my Spring town is always looping on 4/2/2013, 4/2/2014, then 4/7/2014)
if that villager has a birthday within or even close to that month, they are much much less likely to move.
Especially so if you have talked to them, or you received a BDay invite from said villager.
I have very successfully experimented this on several Shari.
- try not talk to them if you don't have to. If you must, save before starting the convo, then quit without saving.
(this would be handy if you need to verify if a villager is original / from others' void, etc)
- One good way is to go into their houses, hang around for a min, take some pics then leave without talking to them.
In my experiences this make them more likely to move out sooner, if not immediately in the next round.
- if you have previously talked to Stitches and haven't done so since, talk to him briefly again *might* renew his chances of moving.
(as you are on speaking terms again and all that)
- Pick another one or two villagers that you choose to talk to / visit their houses, that way the game will see that you have sort of build up friendship with others and not just Stitches. This will kinda trigger the chance of him moving.
Pardon my wall of text. Hopefully this would be somewhat helpful lol. ^^;;
Congrats on your new cycling town & Good Luck!! <3