Excellence under forcing for atomic classes

Let ${\mathbb P}$ be a c.c.c. forcing notion of cardinality $\lambda$ such that forcing with ${\mathbb P}$ forces Martin's axiom and $2^{\aleph_0}=\lambda$, where $\lambda=\lambda^{<\lambda}>\beth_{\omega_1}$. Let $T$ be a countable first-order theory with atomic model class $K_T$. Forcing excellence conjecture. If $K_T$ is categorical in every cardinal below $2^{\aleph_0}$, then $K_T$ is excellent. This is presented as a further conditional form of the excellence problem, with additional discussion deferred to the cited work.