Hey Michael,
Usually these kind of sites belong to a network that runs multiple sites.. Whois look up in the best option to track the details but if it's also not workout like your case, I submit another business with all the wrong details, IP address, fake email address and wait for the confirmation email. Once I get that, I contact them from my original address.
The other option that I lookout is to search on social media, though the chances are less to find the real pages or accounts but you can contact the people who shared something about them in past. For this site, I searched on Twitter.
If nothing works out, then you can clearly tell your client about the efforts you did. In most of the cases, they appreciate your efforts and you can move on.
Hope this helps!
Umar
