UPDATE!!!
Pattye's gimp is bigger than my old gimp and I could fit the Beader's Secret through it easily.
I'm now an expert at knotting with 3 threads. I wasted an entire little doomathingy of Beader's Secret on this strand of pearls, because I kept cutting the thread the wrong length. I finally went overboard and used 7 times the length of the necklace, and that seemed to be just right / way too much, but at least I didn't run out 2 pearls from the end, GAH.
After restringing with the Orbit clasp the first time.
After restring with the Orbit clasp the second time, this time with gold gimp. I know I'm the only one who will notice, but I think it looks more professional, and will keep the thread cleaner. Plus, I feel like the clasp looks more anchored to the pearls this way, too.
I swear this necklace feels like it gets longer every time I restring it, but I think that's because I always make a mess of my first attempt.