Thanks so much for the response Ryan. Lots of good advice. His problem/opportunity isn't just changing architecture, unfortunately. If his site were already "hosted" at the main domain, then I wouldn't be afraid of him dropping from the rankings. But it seems that the search engines are recognizing the site.squarespace.com domain instead of the site.com domain that it is supposed to redirect to.
My sense is that the right thing for him to do long-term is to fix it, and make the necessary improvements to regain the position. It can't be good for potential customers to see the site.squarespace.com result in the serp's instead of his actual domain.