Tchebyshev transform conjecture for Gorenstein* posets

Let $P$ be a Gorenstein* poset, meaning an Eulerian poset that is Cohen–Macaulay, and let $T(P)$ denote its Tchebyshev transform. Gorenstein transform conjecture.* If $P$ is Gorenstein*, then $T(P)$ is Gorenstein*. The conjecture would produce new examples of Gorenstein* posets through the Tchebyshev transform. The source attributes it to Hetyei and gives no resolution.