The bic-III excenter-locus conjecture

Let $P_1P_2P_3$ be a bic-III family of triangles inscribed in an outer circle $\mathcal{C}$, with each side tangent to a distinct in-pencil circle, and assume all four in-pencil circles are distinct. The excenters are the three excenters of the triangle. The bic-III excenter-locus conjecture. Over the bic-III family, the excenters sweep three distinct non-conic curves. This is an experimental observation about the three excenter loci in the bic-III family, and no proof or resolution is supplied.