I just recently posted three towels where I added a design just to the band. I didn't have a problem. I used a med weight cut away stabilizer.
Could you possibly cut away the portion where your design will stitch? Hugs. Na W
I have often stitched on the bands and have never had any problems. Needle goes through easily.
I don't stitch onto the bands. I make my design end about 3 inches above it. I noticed (when I first started embroidering) in the catalogs and such that do embroidery, that they don't stitch on the bands either.