Shouldn't unravel if it had enough twists in it. Flemmish strings need a twist or so every inch to stay intact. Do you know what your brace height should be? I would guess about 8". It could be that your new string stretched, which is pretty normal when you first start to use it, and needed to be twisted up some to keep the brace height where it should be. It sounds like you're using the right string. I would guess that if it's coming unraveled, someone who knows how to make strings could fix it for you. Anyone around NC want to help Turlock out?
(Sorry Bud, you beat me to the post!)