Is there a way to control or direct the growth of Ceratostigma plumbaginoides - autumn leadwort- in a perennial border?
Your idea of a barrier is a good one. A metal barrier would probably be the best choice as it won't rot, unless you use a rot-resistant wood like black locust. It should go down at least 6 inches and be a couple of inches high out of the ground. The plants may try to climb over the barrier but with the use of a good steady barrier, a lawn edger or weed whacker should keep them in bounds but obscure the barrier.