I've tried the moving folders option, but no such luck. The metadata is working correctly in the desktop search, so I don't think it's the files themselves.
I think the only sure fire way to get the app to ask the search indexer again is to uninstall it and then reinstall it. As for the search indexer itself, you should be able to go into the folders in File Explorer on the desktop and see if it's actually properly indexing the metadata for those files (i.e. searching artist:"Jason Mraz" should return only files where Jason Mraz is in the artist metadata tag, and any files it doesn't pick up aren't being indexed properly). You could force an entire rebuild of the Windows Search Indexer database, but deleting folders should do.
Try maybe moving the files into a non indexable location (like a memory stick), and then moving them back, possibly into a different folder?
I'll try uninstalling the Music app and letting you know how it goes.