Pappas–Rapoport flatness conjecture for the symplectic matrix scheme

Let $P$ be the scheme of block matrices defined by the equations in the source: its matrices have the form $\left(\begin{smallmatrix}a&b\\0&{}^ta\end{smallmatrix}\right)$, with ${}^tb=-b$, $Q(a)=0$, and the prescribed characteristic polynomial. Let $F/F_0$ be the totally ramified extension and let ${\mathcal O}_{F_0}$ be its base ring.

Pappas–Rapoport flatness conjecture. The scheme $P$ is flat over

$$\operatorname{Spec}{\mathcal O}_{F_0},$$

with reduced special fiber.

If true, this would imply flatness of the associated naive local model and provide a special case of the broader ramified local-model flatness conjecture. The supplied source gives no resolution.