I'm not sure that this will work but you can try by first making a backup of the QVPR. That way you can restore the current setup if things go south.
- Shutdown the Publisher (QDS service) and Management Service
- Copy your folders and files to the new NAS, but leave the old one available for a while.
- Edit a QVPR file called SourceDocumentFolderResource.xml. At the bottom it lists all Source & User folders and assigns GUIDs to each one of them. The Publisher and Management service only use those unique identifiers to link tasks and documents to paths.
- Modify those paths that have FileType="Source", save the file and close your editor.
- Restart your services and check QMC->System->Setup->Distribution Services->Your QDS->General->Source Folders.
This may also work by simply changing the Source folders in QMC with a running QMS, but I'm not sure that when you change source folders, the linked tasks will survive...
If the result is not good, shutdown the services again, resotre the copy of the QVPR and start the services again.