Gedeon's dominance conjecture for matroid Kazhdan--Lusztig and Z-polynomials

Let $\mathsf{M}$ be a loopless matroid of rank $k$ on a ground set of size $n$. Let $\mathsf{U}_{k,n}$ be the uniform matroid of rank $k$ on $n$ elements, and write $A(x)\preceq B(x)$ when $B(x)-A(x)$ has nonnegative coefficients. Gedeon's dominance conjecture. The inequalities

$$P_{\mathsf{M}}(x)\preceq P_{\mathsf{U}_{k,n}}(x),\qquad Z_{\mathsf{M}}(x)\preceq Z_{\mathsf{U}_{k,n}}(x)$$

hold. Thus uniform matroids should maximize coefficient-wise the Kazhdan--Lusztig and $Z$-polynomials among matroids with fixed rank and size. This conjecture is attributed to Gedeon, with an equivariant version attributed to Proudfoot, and remains open in the supplied source.