Effaceability of derived ordinary parts for locally admissible representations

Let $G$ be a reductive group, let $P^-\subset G$ be the opposite parabolic subgroup, and let $\mathfrak{Rep}^{\textnormal{ladm}}(G)$ denote the category of locally admissible representations. For $i>0$, $\textnormal{H}^i\textnormal{Ord}^G_{P^-}$ denotes the $i$-th cohomological ordinary-parts functor and $\textnormal{R}^i\textnormal{Ord}^G_{P^-}$ its right-derived functor in this category.

Effaceability conjecture. The functors $\textnormal{H}^i\textnormal{Ord}^G_{P^-}$ are effaceable on $\mathfrak{Rep}^{\textnormal{ladm}}(G)$ for $i>0$. Consequently,

$$\textnormal{H}^i\textnormal{Ord}^G_{P^-}\simeq\textnormal{R}^i\textnormal{Ord}^G_{P^-}$$

for $i>0$, where the derived functors are computed in $\mathfrak{Rep}^{\textnormal{ladm}}(G)$.

This is stated as one of the conjectural inputs for computing derived ordinary parts and is identified in the source with a question of Emerton; the supplied text gives no resolution status.