I don't know if it counts since it's remixes rather than the original recordings, but there's a site called
Anime Remix where various people take songs from anime
and other animated series and make remixes out of them. The catch, of course, is that the songs have to have been originally composed for the work. "Fly Me To The Moon" doesn't count because it wasn't composed for NGE, for example.
And yes, I said they also make remixes from non-anime animation. There's Disney, there's Bluth, there's Bagdasarian, and more, along with Natsuki Takaya, for example.
The idea is similar to
Overclocked Remix, where they do the same thing with video game music.