Carolyn i did not know that asparagus ferns had thorns! It's been years since I grew them....i guess my knowledge of the thorns got lost in the mists of time. Do you know how they reproduce? I seem to remember seeing orange seed berries on them. Maybe they just throw lots of seed around? How about the roots, are they tenacious? I would still be tempted to pull the whole shebang out and start over. That hedge looks like it needs to be renewed anyway.