I have a feeling the needle you were/are using may be the culprit. I use Gutterman, Coats & Clark, Americana. Probably my least favorite is Coats & Clark but even that is okay most of the time. All are specifically labeled 'hand quilting' thread. It does make a difference. I, too, treat my thread with Thread Heaven while quilting. I have had some minor issues with shredding on occasion. Find that it's usually the eye of my needle causing the problem.
I have also very successfully used hand quilting thread to sew down the binding as well. I think my stitches are about as close to invisible as possible. Honestly haven't noticed much of a difference between using the hand quilting or general sewing thread for that purpose. All depends on color and what's handy for me.