Is there an easy way to get rid of many, many lily of the valleys?

I wish! since the travel by shallow (sort of) roots you can use a hoe to scrape them up. It is back breaking work. My initial thought was napalm, just kidding.

I saw this on Craigslist with daylilies: Free Lily of the Valley plants. You dig them, you can have them! You can also call a non-profit local agency and offer the same deal to their landscaping crew!

I wish had your problem! I live in central Texas and have planted them over and over again and have to see one sprig of green from the plantings. I'm assuming you're somewhere north of me. (My MIL grew them in Pa and my husband loves them.)