We use Scotch 3M sticker remover markers. It is similar to the goo gone concept, but the marker makes it a lot easier. No saturating, just start scrubbing the adhesive with the marker. Go around the frame a few times, and then just pull off the excess with a makeup remover pad. Once over with alcohol---perfect frame.
I think you're on the right track--a perfect frame is the key to a professional repair.