Finiteness conjecture for exceptional bundle slope vectors

Let $Y$ be a smooth projective surface such that $K_Y$ is ample, $H^2(\mathcal T_Y)=0$, $H^{2,0}(Y)=0$, and $\pi_1(Y)=0$. Let $S$ be the set of slope vectors $v(F)=c_1(F)/\operatorname{rk}(F)\in H^2(Y,\mathbb Q)$ of exceptional vector bundles $F$ of rank greater than $1$ that are slope stable with respect to $K_Y$ and whose degree $c_1(F)\cdot K_Y$ is coprime to $\operatorname{rk}(F)$, modulo translation by $H^2(Y,\mathbb Z)$, multiplication by $\pm1$, and the action of the monodromy group. Finiteness conjecture. The set $S$ is finite. Equivalently, the ranks of exceptional bundles $F$ on $Y$ which are slope stable with respect to $K_Y$ and have degree coprime to the rank are bounded. This conjecture concerns the finiteness of exceptional bundles arising from the boundary divisors of the moduli space of stable surfaces; the source gives no resolution of the conjecture.