Weyman's multiplicity-free conjecture: Schur-representation-finiteness and MF

Let $A$ be a finite-dimensional algebra. Say that $A$ is Schur-representation-finite if it has only finitely many indecomposable representations with Schur endomorphism algebra, and let MF denote the multiplicity-free property defined through dense orbits in representation varieties.

Multiplicity-free conjecture. An algebra is Schur-representation-finite if and only if it is MF.

This is the unrestricted form of the conjecture attributed to Weyman, extending the corresponding result or conjecture beyond tame algebras. The source gives no resolution.