The ACC conjecture for primitive ideals of Witt and Virasoro enveloping algebras

Let $\g$ be one of $\W{-1}$, $W$, or $\Vir$, and let $\Ua(\g)$ be its enveloping algebra. ACC conjecture. The algebra $\Ua(\g)$ satisfies the ascending chain condition on primitive ideals. The source lists this as another consequence that would follow from surjectivity of the strong Dixmier map, and it would rule out infinite strictly ascending chains of primitive ideals in these enveloping algebras.