I haven't tried King Kong yet. But, for many current dvds with authoring intended to prevent backups AnyDVD succeeds where dvd43 fails. So, yes I would try it again with AnyDVD.
My other comment is that if you are using 1Click and a separate CopytoDVD as your burner, then you are not using the latest 1Click and there's a possibility you have Patin-Couffin drivers and a CopytoDVD version that are "out of sync" with your 1Click. That's especially true if you downloaded CopytoDVD directly from VSO.