Saul Jaramillo takes care of the nuts and bolts of my yard and last year he showed me a technique to renew Agapanthus. I was skeptical, but it worked like a charm. It's a simple cut-to-the-ground-and-let-it-regrow technique. Since I have so much Agapanthus I've had to learn to live with them and make them look their best. I'm gradually replacing them, but I can't foresee a time when I have none, so here's a photo of three plants at various stages of renewal.
Foreground and center against the fence are two that are recently coppiced. Mid ground is one that was coppiced about two weeks ago, and background left and right corners are some that will be coppiced in a few weeks time. Distributing the coppicing over a few weeks keeps some greenery in place at all times. Coppicing can be done with a shovel.