Good questions. I did in fact speak with the host, and they were more than happy to host my family and I. Unfortunately, they didn't know of anything to try differently on their end to allow the booking attempts to process. I even tried, with the hosts permission, selecting only 8 people as the group size when attempting to book and was still denied.
Clicking the "learn more" link on the party risk pop-up, it mentioned something along the lines of the booking being short notice as potential concern. It's a whole month away though so I'm guessing that's just generic info.
At this point, I'm assuming it's due to lack of reviews as a guest like ya'll have suggested, despite Airbnb support ambassadors saying otherwise. I've given up and our family is getting separate hotel rooms. It is what it is. Maybe I'll give Vrbo a try instead.