If the Client Files Members has a distribution list, and you are running Outlook, you should be able to open the Group up in Outlook - that should tell you who is in there. However, if you choose to move your documents to a new site, you can do that, but keep in mind that depending on how you do it, you might lose metadata. If the libraries have custom metadata columns, those will have to be recreated. If there are versions attached, you will lose those as well. Also, your name would replace the creator, and the created/modified date would change to the time you moved them - that might not be a big deal with your users, but you might want to let them know.
Is it possible since you recreated all those groups and set your libraries to them that you can remove the AD groups from the site permissions? Authenticated users is added by default but you should be able to remove them.
