The BEC bound for sandwiched Rényi conditional entropy

Let $X_1,X_2$ be binary random variables with quantum side information $B_1,B_2$, and let $\tau$ denote the product construction in which the output is $X_1+X_2$. Write $\widetilde K_\alpha^\downarrow(X_i|B_i)$ for the corresponding sandwiched Rényi conditional quantity, and let $\delta_\alpha^H$ denote the parameter appearing in the binary erasure-channel bound. The BEC bound. For $\alpha\in(0,2]\cup[3,\infty)$,

$$\widetilde H_\alpha^\downarrow(X_1+X_2|B_1B_2)_\tau\leq\frac{1}{1-\alpha}\log\left(\frac{(\delta_\alpha^H-\widetilde K_\alpha^\downarrow(X_1|B_1))(\delta_\alpha^H-\widetilde K_\alpha^\downarrow(X_2|B_2))}{1-\delta_\alpha^H}\right)+\delta_\alpha^H.$$

For $\alpha\in[2,3]$, the same statement holds with the inequality direction reversed; for $\alpha\in\{2,3\}$, equality holds. The conjecture is intended as the Rényi-information analogue of the binary erasure-channel bound, but the supplied text does not provide a resolution for general $\alpha$.