Conjecture on intermediate values of Mahler measure

Let $M_{\inf}$ be the limit infimum of the Mahler measures ${\rm M}(\alpha)$ as $\lvert\alpha\rvert\to1^+$, and let $\Lambda$ be the limiting constant introduced for the relevant family of reciprocal algebraic integers. For any $\nu_0\in[M_{\inf},\Lambda)$, consider integer monic irreducible polynomials $H_m(z)$. Intermediate-value conjecture for Mahler measure. There exists a sequence $(H_m(z))_m$ such that

$$\lim_{m\to+\infty}{\rm M}(H_m)=\nu_0.$$

The conjecture proposes that every intermediate value below $\Lambda$ is attained as a limit of Mahler measures. The source offers this as a formulation motivated by compactness of the beta-shift, with no resolution evidence supplied.