I am really bad when it comes to re-potting. I would probably soak the roots really well so they are more pliable and then gently pop the whole thing into the next size pot or basket, after carefully picking out old bark. But as I said, I probably could use some lessons on re-potting into bark. I don't like to bury fresh roots too deeply, they seem to grow happy as is.
I don't really worry about those pots. I use whatever ....