Pull, pull, pull, use weed-wacker to give you more time if needed, before seeds ripen. I have the same problem and have spent hours pulling this plant this year. The cuteness of this plant lulled me into not taking the few I saw the past few yrs seriously. Now I've got thousands. I pulled about 10 gallons of them up today. If you can get 'em all up before the seeds drop, it should be a lot easier next year.
At least the seeds don't seem to go very far. Like you said, they need to be removed completely, not half-heartedly. Start with your most "prized" spots and keep them clean, moving into other areas as you have time.
If you have areas with nothing but CB, you can smother them easily with cardboard covered with mulch.