The local model flatness conjecture for parahoric unitary moduli

Let $(r,s)$ be a signature and let $I\subset\{0,\dotsc,m\}$ be nonempty. Let $M_I^{\mathrm{naive}}$ be the naive local model, $M_I$ the closed subscheme cut out by the wedge and strengthened spin conditions, and $M_I^{\mathrm{loc}}$ the scheme-theoretic closure of the generic fiber in $M_I^{\mathrm{naive}}$. Local model flatness conjecture. The scheme $M_I$ is flat over $\operatorname{Spec} O_E$; equivalently,

$$M_I^{\mathrm{loc}}=M_I.$$

The conjecture concerns whether the additional local-model conditions exactly describe the flat closure of the generic fiber; the source notes that the strengthened spin condition implies the Kottwitz condition, while the general implication to the wedge condition is not known.