Countable coheir detection conjecture for commutativity

Let $T$ be NIP or dp-minimal, let $M\models T$ be countable, and let $q\in S_y(M)$. A coheir of $q$ is a global type finitely satisfiable in $M$ extending $q$.

Countable coheir detection conjecture. There is a countable subset $Q\subseteq S_y(\mathcal U)$ of coheirs of $q$ such that, for every invariant type $p$, if $p$ commutes over $M$ with all types in $Q$, then $p$ commutes over $M$ with every coheir of $q$.

The proposed statement is a sufficient condition for proving the central conjecture in dp-minimal theories. The supplied text gives no resolution.