I'm not looking for a new menu entry, rather a button on (one of) the now playing screen(s). The most obvious use is in-car, so perhaps the in-car screen.
This might be an option, provided that the dialog has the current song's tags after showing up.
Any reason apart from spending the time? What if someone did it on their own?
Why? A couple of situations in which overrides are extremely useful: Misnamed tags (on our or the provider's side). This includes the mentioned wikia problem, capital/small letters issues (no redirects here if name is Cyrillic [1]) or situations where the band changed its name.
Live tracks. Suppose you have a track "I Am The Law (Live)". You can override it and have the lyrics for the real track loaded. Ideally, you would use a regular-expression-based override, but specifying the overrides in a per-track manner is better than no lyrics
Another reason to use it: if we know that artist "Эпидемия" is in fact "Эпидемия_(Epidemia)" we load 1 page instead of 3 per track.
The 3-page strategy would work great if being supplemental but on its own is merely a workaround.