Yes, I would combine this with a couple of fake entries, and when those show up on their site, you file DMCA claims with google, and with their hosting provider

Yes, I would combine this with a couple of fake entries, and when those show up on their site, you file DMCA claims with google, and with their hosting provider. An american company has no choice but to shut their site down under threat of DMCA claims. If the site gets back up, add another fake entry, and do it again when they scrape you, until they give up.