Are there counterexamples to the following:
Given two varieties $A$, $\tilde{A}$, both defined over $\mathbb{Q}$, one of which, say $A$, is a Shimura variety. Then, every isomorphism **defined over $\overline{\mathbb{Q}}$**
$$f: A_{\overline{\mathbb{Q}}}\rightarrow \tilde{A}_{\overline{\mathbb{Q}}}$$
can be twisted to an isomorphism
$$f^{*}: A_{{\mathbb{Q}}^{\text{solv}}}\rightarrow \tilde{A}_{\mathbb{Q}^{\text{solv}}}$$
defined over ${\mathbb{Q}}^{\text{solv}}$, the solvable closure of $\mathbb{Q}$.

If one could show that this holds at least for genus-one curves, this would imply a long sought-after conjecture that every genus-one curve over $\mathbb{Q}$ has a solvable point (every genus-one curve is isomorphic over $\overline{\mathbb{Q}}$ to its Jacobian, which is an elliptic curve over $\mathbb{Q}$ and has solvable points), so I want to ask: Are any results known about this in higher genus?

To my knowledge, the best result to this day is that of Ciperiani and Wiles (https://www.ma.utexas.edu/users/mirela/solvable.pdf), who give an affirmative answer in the case that the genus-one curve is locally nontrivial and semistable, but neither of these conditions seems to be necessary.