[Legate of Amon Lanc]

Well it does not sound that bad, Lommy, and if I had to accept that Ungoliant is not an Ainu but had to find a definite answer to what she is in Eru's creation, I could go along similar lines as you do. So what if she is not outside Eru's creation, but outside the Music? That would fit very well with the idea of un-Light, as opposite to what goes through the Music. We know Eru placed his own devices inside the Music, yet no one said he could not have done? made? anything else. That could go somehow even with your idea of "being born from the Darkness", however we have to consider one thing that outside the Music (and Arda, subsequently) there was only the Void, which is not even Darkness, not even Un-Light, but it is nothing.

Taking into account that the Ainur were definitely the first thing to be created by Eru, Ungoliant, whatever she was, if she was not one of them, had to be created later. As for Melkor creating her in the Music, it is possible (maybe she in the Music she would have been some attempt to destroy the Light that went wrong and turned away even from him, however in that case again I would see it more logical that she was an Ainu), but the idea of her being something else outside the Music seems more plausible to me, if I had to choose.