Thanks, that's what I'm inclined to do, too.
I picked away at it with chop sticks, and only managed to break off a couple more nice healthy roots. So I'm finished cleaning and messing with it and will just pop it into the new pot after dusting with cinnamon.
As you say, not particularly worried about the clay pots, but I do wonder what might be in that terracotta coloring they're using. At least with the solid terracotta clay, there's no chemical concerns.