The Prym-image conjecture for the divisor $D(\mu;3)$

Let $\mathcal{R}_6$ be the moduli space of Prym curves of genus $6$, let $\mathcal{A}_5$ be the moduli space of principally polarized abelian varieties of dimension $5$, and let $\mathcal{P}_6\colon\mathcal{R}_6\to\mathcal{A}_5$ be the Prym map. Let $D(\mu;3)\subset\mathcal{R}_6$ be the divisor considered above. Its slope is measured on $\mathcal{M}_6$, the moduli space of smooth curves of genus $6$. Prym-image conjecture for $D(\mu;3)$. The restriction $\mathcal{P}_{|D(\mu;3)}$ of the Prym map is generically one to one. Moreover, the pullback $\mathcal{P}^{-1}(\mathcal{P}(D(\mu;3)))$ consists of $D(\mu;3)$ and a second divisor that is the pullback of a divisor on $\mathcal{M}_6$ of slope

$$\frac{2\cdot 547}{137}\approx 7.985.$$

The conjecture is motivated by the computed pullback and pushforward of $D(\mu;3)$: the difference has boundary coefficients whose ratio suggests that the second component comes from a divisor on $\mathcal{M}_6$.