Download icon appears next to songs in iTunes, but files already downloaded

See Empty/corrupt iTunes library after upgrade/crash. Unfortunately once iTunes thinks it no longer has a local copy of a track it can be difficult to persuade it otherwise short of adding it to the library again, which might confuse things further.

tt2

The process is simple. Rename a file, copy another file, rename that. Job done. It only becomes slightly more complex if the last backup of the database is out of date in which case bringing it up to date isn't that hard, and less effort than what you're planning. If you're running on a Mac and you have Time Machine copying your iTunes Library.itl file you should be able to restore a version of it from just before things in your library went cloudy and not have to do any maintenance at all.

tt2

OK. Ideally you should backup the state of your iTunes library folder (I assume this on your Mac) and the iTunes Media folder on the NAS before you do anything else. iTunes may not always play nicely with NAS and recovery can be difficult or impossible if anything goes wrong.

To make your library reflect the contents of your media folder first sign out of your Apple ID. Then use File > Add Folder to Library to add the contents of the media folder into the library. Anything that iTunes already knows about will be ignored, everything else should be added, and, if you have the Keep organized option enabled, may be moved to reflect tag details as required. Finally sign back into your Apple ID. Download anything that remains in the cloud. If all is well update your backup.

tt2