Well if the files have at least Artist and Album metadata, a one line action can move the files into an Artist/Album/file structure. At that point you'll have a structure which is far easier to work with and possibly evaluate. Im not sure what 'three' directories you want to end up with. There is no way to determine what is a bona fide single and what is a single track from an album.

There's a lot of potential issues here.

If you have stuff in folders then an attempt can be made to match entire folders to a single album on MusicBrainz. However it gets very dodgy in that there are many albums where a release has more tracks than another. Often an album in one country has one track more or less than the same release in a different country. If a track is missing in themiddle of an album it's clear that it is incomplete. However if an album has 10 tracks and some releases have 11 it gets more difficult. Not impossible ... just more difficult. To make matters even more difficult is the fact that some releases have the same number of tracks but have one track which is different. All of the previous points would require that every possible match for a release would have to be examined. Even if that was done, the match attempts would have to be fuzzy as the chance of every track having the exact same title as found in the MusicBrainz DB is slim over a large enough number of tracks.

Fingerprints have nothing to do with album contained tracks or singles. Fingerprints are constructed by examining the audio stream and are then matched against the AcoustID database. If a match is found a long list of potential matches can be returned. The returned metadata for each potential match refers to a recording and release in the MusicBrainz database. Even matching a known single is difficult as singles are often re-released on an album. If the audio is the same ... the fingerprint will be the same. If I use AcoustID for a match to Border Reiver by Mark Knopfler the fingerprint matches a track on a Greatest Hits album with 33 tracks, on the album Get Lucky with 17 tracks and on an album called Get Lucky with 11 tracks.

It seems to me that an attempt should be made to match any album which would end up as complete. The action statements tend to look for a single release containing all tracks but this does not necessarily end up with an album with the same number of tracks.

Again, none of the above makes it an impossible task just a very difficult one.