I you wanted to, you could probably replace the serving on your string with a smaller diameter serving that would fit your nocks. I like to adjust serving size to fit the nocks, since most nocks have a standard sized opening, and it is a pain to adjust all the individual nocks.
Or, going down to 14 strands might do the trick. Certainly, 14 strands is adequate, or even 8 if you use some of the newer string materials. With 8, you would have the opposite problem, of having to build up the serving.