Equidistribution conjecture for anomalous shadow lines in the receptacle

Let $E/\mathbf{Q}$ be an elliptic curve of analytic rank $2$, let $p$ be an odd prime of good ordinary anomalous reduction, and let $K$ be an imaginary quadratic field satisfying the Heegner hypothesis for $E$, such that the analytic rank of the twisted curve $E^K/\mathbf{Q}$ is $1$ and $p$ splits in $K$. Let $H$ be the receptacle, with $H\subseteq E(\mathbf{Q})\otimes \mathbf{Z}_p$, and let $L'_K$ be the shadow line and $\mathcal{S}$ the distinguished shadow line. Filtered equidistribution conjecture. If $E$ does not have a rational $p$-isogeny, then the shadow lines $L'_K$ that coincide with $\mathcal{S}$ in $H\otimes \mathbb{F}_p$ are equidistributed in $H$. The claim refines the preceding anomalous-reduction distribution question by conditioning on the distinguished mod-$p$ shadow line; the supplied text gives no resolution, so the status remains open.