Mishou's joint strong universality conjecture for Lerch zeta-functions

Let $\alpha$ be a transcendental real number with $0<\alpha<1$, and let $\lambda_1,\ldots,\lambda_r$ be distinct real numbers satisfying $0\leq\lambda_j<1$. Mishou's conjecture. The joint strong universality holds for

$$\zeta(s,\alpha,\lambda_1),\ldots,\zeta(s,\alpha,\lambda_r)$$

in the region $D(1/2,1)$.

This conjecture extends known measure-theoretic and explicit families of parameters to all distinct parameters for a fixed transcendental $\alpha$. The source does not give a resolution.