I think you're right. The circumcentre equation is just more complicated than the centroid calculation I was imagining. They're doing exactly what I had suggest

I think you're right. The circumcentre equation is just more complicated than the centroid calculation I was imagining. They're doing exactly what I had suggested in the third paragraph. There may also be a nice derivation of the triangle centre on the sphere coming from quaternion math that would avoid renormalization. I wonder...