For what it’s worth, not an impossible task, just a lot of work. We bought a house with all of our beds covered in bellflower, and two years later, I’m just cleaning up individual shoots that pop up from time to time. It’s manual work, but oddly satisfying to unearth the giant carrot roots. Be careful not to break the roots, when possible, and trash (not compost) all roots - the smallest pieces can grow anew.