Constructibility and openness of F-rational fibers over higher-dimensional bases

Let $D$ be a higher-dimensional base and let $X\to\operatorname{Spec}D$ be a general finite type family. For $t\in\mathfrak{mSpec}D$, consider the property that the fiber $X_t$ is $F$-rational.

F-rational fiber-locus conjecture. The locus of $t\in\mathfrak{mSpec}D$ for which $X_t$ is $F$-rational is constructible. If the family is flat and proper, or sufficiently local, then this locus is open.

This conjecture extends openness results for $F$-rational fibers over spectra of Dedekind domains to higher-dimensional bases. The source does not provide a resolution.