Thanks for the advice, everyone. I'm glad I'm not the only one with this problem. A friend of mine who has experience with sewing told me that she thought that over time, the strands would knot up or something and the fraying would stop. But that's clearly not happening here.
I didn't hack these myself, FWIW. This is how they came from J. Crew.
Runs with Scissors, I will check out the Fray Block after I give my jeans a haircut!