Weyman's dense orbit conjecture for triangular algebras

Let $A$ be a triangular finite-dimensional algebra, meaning that its ordinary quiver has no oriented cycles. For an ideal $I$ of $A$, write $A/I$ for the corresponding quotient algebra, and say that an algebra is DO if its representation varieties have dense orbits.

Dense orbit conjecture. The following statements are equivalent:

1. $A$ is representation-finite.
2. For any ideal $I$ of $A$, the algebra $A/I$ is DO.

This conjecture relates representation-finiteness of triangular algebras to the dense-orbit property for all their quotient algebras. The source presents it as a conjecture of Weyman and gives no resolution.