Atomic saturation conjecture for stable theories without the finite cover property

Let $T$ be a theory with elimination of quantifiers, and let $M$ be a model of $T$. For a filter $D$ on $\lambda$, write $M^\lambda/D$ for the reduced power and $\aleph_0^\lambda/D$ for the corresponding ultrapower cardinal. Assume that $T$ is stable without the finite cover property and that $D$ is a $(\lambda,\aleph_0)$-regular filter on $\lambda$.

Atomic saturation conjecture.

$$M^\lambda/D\text{ is }(\aleph_0^\lambda/D,\text{ atomically})\text{-saturated}.$$

The claim is stated in the context of questions about atomic saturation of reduced powers and the stable case. The source does not provide a resolution, so the conjecture remains open.