Hi again John,
Fabric does that going around corners ans sewn seams running long the stems are common. Cut the excess off about an inch away from the stem and parallel to it. Heat-seal the cuts if you're working with synthetic fabric. Fold the edge once, then fold again, putting the edge of the first fold against the stem. Sew the fold to the fabric. I hold the longitudinal tension in with staples, removing them one by one as I fold and sew.