Landweber–Stong depth conjecture for finite general linear groups

Let $H$ be a subgroup of $GL_n({\mathbb F}_q)$ acting on $S={\mathbb F}_q[\mathbf{x}]$, and let $D_{n,j}$ denote the Dickson polynomials. Landweber–Stong conjecture. The depth of the invariant ring $S^H$ is the maximum integer $i$ for which

$$D_{n,n-i},D_{n,n-i+1},\ldots,D_{n,n-2},D_{n,n-1}$$

form a regular sequence on $S^H$. The source notes that this conjecture was proven when $q=p$ is prime by Bourguiba and Zarati; the general case is not resolved in the supplied text.