Ultimately, I think what works best is how people interested in your works are going to be looking for it, and I think using 'filk' as fandom is the best is the best solution at least for now - I'd say it's the equivalent of using RPF as a fandom tag.
From a reader's perspective, I think using the original song as fandom would be just confusing because IMO the filks aren't really about the song.
For example, I've written a filk about Babylon 5 to Queen's "Bohemian Rhapsody", and I think that it would be of more interest to fans of babylon 5 than to fans of Queen, and might even irritate people who click on the link expecting to find works about the characters in "Bohemian Rhapsody". Does that make sense?
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From a reader's perspective, I think using the original song as fandom would be just confusing because IMO the filks aren't really about the song.
For example, I've written a filk about Babylon 5 to Queen's "Bohemian Rhapsody", and I think that it would be of more interest to fans of babylon 5 than to fans of Queen, and might even irritate people who click on the link expecting to find works about the characters in "Bohemian Rhapsody". Does that make sense?