The Clifford-index slope conjecture for special linear-series loci

Let $X\to B$ be a general family of genus $g$ stable curves whose general member has Clifford index $\mathfrak{c}$, and let $B$ be a general curve in $\overline{\mathcal D}^r_d$. Clifford-index slope conjecture. For $\mathfrak{c}\ll g$, the slope satisfies

$$\frac{\delta_X}{\lambda_X}\leq \left(6+\frac{2}{\mathfrak{c}+1}\right)+\frac{2\mathfrak{c}+4}{g}.$$

This extends the observed slope bound for plane quintics and is motivated by the fact that the Clifford index of a $d$-gonal curve is at most $d-2$. The claim concerns general families and general curves in loci defined by a $g^r_d$, and remains conjectural in the supplied source.