So I’ve discovered that this is mostly operator error. If anyone else has had this problem, maybe this will help.
I was just pulling hard on the string, and that was actually locking it in tighter. I found that if I make sharp quick tugs back and forth, parallel to the gap, I can almost always get the string to come loose.
Probably that only that fails, when there is an axle knot hidden inside.
Thanks for the tip @Myk_Myk, I feel like I may have caused some separation on one of my throws doing the same kind of tug. The quick tugs will be what I try now,.