Your last suggestion is the best. You need a new end of yarn and that can come from another ball of yarn or it can be the other end of the ball that you are using now. The pattern is going to have you complete both sides of the neck shaping at the same time with two separate ends of yarn (so don't cut anything yet).
Knit across to the sts to be bound off, drop the strand of yarn you are working with, start knitting sts for the bind off with a new end of yarn, bind off 10sts total, and continue to knit across the other side of the neck. Purl back with this second strand up to the bound off sts, drop the yarn, pick up the strand conneted to the other shoulder and purl across that shoulder. Doing it this way ensures that the shoulder shaping is the same on both sides.
Glad it's working out for you!