The domain was previously one of several domains pointing at a single website (not a 301, the domain name in the address bar remained whatever you typed in). Could this be what's causing the problem? If so, what can I do about it?
N.B. I don't think this is a sandbox issue. The site isn't in a commercial area, and I've been able to get a similar site to rank well in a short space of time.
I've seen all manner of ranking variation when it comes to "previously owned" or "old and transferred" domains.
Blanket rules that would penalize a domain for a use such as you describe would not reflect the best intelligence when it comes to ranking a website that "is a thing new". Perhaps wrongfully, I give Google credit for being a bit smarter than that. (Let the lashings begin.)
I would look elsewhere or simply assume the back history of the domain is only 1 of many variables at play. As best I can tell Google is still focused on the merits of link votes as the foundation of its ranking algorithm. That would be where I would focus: rate of link growth, neighborhood of links, authority of links, tld of ranking sites in realm (.edu?), tld of IBLs for ranking sites, etc.