The interlacing conjecture for Z-polynomials of nice matroid families

Let $\{M_d\mid d\geq 0\}$ be a nice family of matroids, and let $Z_d(t)$ denote the $Z$-polynomial associated with $M_d$. For polynomials with real roots, say that $f(t)$ interlaces $g(t)$ when their roots satisfy the interlacing inequalities in the source. The interlacing conjecture. For every $d$, $Z_d(t)$ interlaces $Z_{d-1}(t)$.

This conjecture parallels the proposed interlacing relationship for matroid Kazhdan–Lusztig polynomials. The source states that the corresponding Kazhdan–Lusztig interlacing conjecture remains open, but gives no separate resolution status for this $Z$-polynomial version.