The issue with folders containing thousands of tracks is one of context. Both the DIscogs and MusicBrainz wizards work on releases (albums) rather than tracks. Again, this is because matching is better when dealing with more than a single track.
The first step in these situations is somehow dividing the large folder in many smaller folders which makes it easier to work with.
You could use AcoustID in the UI where you could see potential matches. However, this will soon become tiresome with thousands of tracks.
One approach would be to have an action which would fingerprint, access AcoustID and make individual track based decisions on matches. Once this is done a subsequent action could move all the files to grouped folders. This would certainly be easier to work with.
Acoustic fingerprinting is not an exact science ... false matches will be made when processing thousands of files. For this reason, I suggest saving the initial basic metadata in the files or in a database (or both). The space overhead for a few additional tags in each file is insignificant and they can be removed at a later time. The matching process can update the database so that you could look at it at your leisure. In fact the process could even save the matching results to the database and not actually save them to the files. Lots of ways to go.
This is the only way to handle the mess in a more or less automated manner.
One question is are there sub-folders containing tracks inside the Various folder? It doesn't really matter other than which mode the action should be run.
If you wish I can knock off an action to get you started. You could then look at the database and se if you're happy with the results.