Rosalie Maggio mentioned CatalogChoice several times and I finally went to look at the site. I added the most recent catalogs that I hadn't had the get-up-and-go to actually call and cancel through the browser entry system; pretty simple and easy. Then I looked at their subscription service to stop info-brokers from selling your data; seems a little expensive and kinda overkill.
Then I found MailStop Mobile, which is an iOS (maybe android, too -- dunno) app that lets you take a picture of the mailing label (mailing label, sender name, customer number) and send it in. Mmmmmmm.
I'm sort of looking forward to this; it might make it possible to stop the single piece mailings, which I had not previously attempted to thwart -- I was only going after catalogs.