The worst fraying I have experienced was with licensed fabric (Eric Carle's Brown Bear and Hungry Caterpillar). It is terribly frustrating.
I have found that careful cutting - squaring up the fabric so that there are not off grain threads to loosen - combined with starch helps a lot when handling fabric. The starch piece isn't going to help once a fabric is washed, though. So if it's in the seam allowance and fraying, once that quilt is washed, the starch won't be there to keep it in place.
Since you've already quilted it and can't add "second" seam, could you add quilting just to the side of the seams to hold it in place? I don't know what else to suggest to correct the problem you are having in this piece.
Regardless of what, if anything, you do to try to fix the problem in this quilt, I would contact the manufacturer to let them know. Send them pictures of a piece of the fabric, if you have a scrap, showing the fraying that you had to trim up as well as a picture of the threads that are migrating in the finished quilt.