Openness of derived tameness in flat families of algebras

Let $X$ be an algebraic variety and let $\mathcal A$ be a flat family of algebras over $X$. Write

$$X_{\mathrm{tame}}=\{x\in X\mid \mathcal A(x)\text{ is derived tame}\}.$$

Openness conjecture. The set $X_{\mathrm{tame}}$ is open in $X$.

The preceding result shows only that $X_{\mathrm{tame}}$ is a countable intersection of open subsets. The conjecture is presented as plausible, but even its analogue for usual tame algebras was not known in the source.