Have you seen the studies from Shannon et al (2015) and Ni Leathlobhair et al (2018)? Those are the two most recent genetic studies to include Carolina Dogs, and both concluded that all CDs tested were of predominantly European ancestry, with a range of 0-35% pre-Columbian/Asian ancestry at the level of individuals. Which is still a high average of pre-Columbian/Asian ancestry for an American dog type from outside the Arctic/Alaska region, but nonetheless paints a pretty different picture from what Brisbin had originally speculated, back in the days before this kind of testing was possible. AFAIK, the only other studies relevant to the CD are a couple earlier, more tentative ones that had looked only at mitochondrial DNA.
Shannon et al: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4640804/
Ni Leathlobhair et al: https://www.researchgate.net/publication/326211519_The_evolutionary_history_of_dogs_in_the_Americas
I know Embark tests for Carolina Dog, FTR. They are fairly generic-looking dogs even when pure, in the sense that any number of mixes with a good dose of spitz and/or herding type in them could wind up looking quite a lot like one.