I do remember moving my home from Aven to guild without paying the Aven rent, so you shouldn't have to wait or pay if you're moving. If you haven't already, try going to your Guild's Town and click Rent Room. When you confirm it, it should automatically close your Aven home and set a new one in the Guild Town with no fee.
Before trying, you should take out all of your furniture and put it in the storage or in your inventory. I'm not sure if it deletes the furniture when you change.