Zilber's trichotomy principle relative to a theory

Let $T$ be a complete theory. Let $\mathcal N=(N,\ldots)$ be any model of $T$, and let $P$ be an $\mathcal N$-interpretable set. Let $\mathcal P=(P,\ldots)$ be an $\mathcal L'$-structure over $P$, for some language $\mathcal L'$, such that every $\mathcal P$-definable set is also $\mathcal N$-definable.

Zilber's trichotomy principle relative to $T$. If $\mathcal P$ is strongly minimal and non-locally modular, then there is an infinite field interpretable in $\mathcal P$.

This is a restricted formulation of Zilber's trichotomy principle. The unrestricted principle is false by Hrushovski's counterexample; the source also records that Castle proved the conjecture relative to $ACF_0$, while the general validity of this relative formulation is not established here.