Unconstrained Hilbert-series conjecture for Koszul Gorenstein algebras

Let $d$ be an integer with $d\gg 0$, let $\pi$ be a permutation of $\{1,\dots,\lfloor d/2\rfloor\}$, and let an artinian Gorenstein Koszul algebra have Hilbert series

$$\sum_{i=0}^d h_i t^i.$$

Koszul Roller Coaster conjecture. There exists such an algebra satisfying

$$h_{\pi(1)}<\dots<h_{\pi(\lfloor d/2\rfloor)}.$$

Equivalently, the first half of the Hilbert-series sequences of artinian Gorenstein Koszul algebras of sufficiently large socle degree is unconstrained. The statement is presented as an open question motivated by the corresponding result without the Koszul condition; no resolution is supplied in the source.