Moretó's subnormalizer conjecture for finite groups

Let $G$ be a finite group, let $p$ be a prime, and let $x\in G$ be a $p$-element. Write $\operatorname{Irr}^x(G)$ for the irreducible complex characters of $G$ that are nonzero at $x$. Define the subnormalizer subset of $x$ in $G$ by

$$S_G(x)=\{y\in G\mid\langle x\rangle\mathrel{\triangleleft\triangleleft}\langle x,y\rangle\},$$

and define the subnormalizer by $\operatorname{Sub}_G(x)=\langle S_G(x)\rangle$. Subnormalizer conjecture. There exists a bijection

$$f:\operatorname{Irr}^x(G)\to\operatorname{Irr}^x(\operatorname{Sub}_G(x))$$

such that, for every $\chi\in\operatorname{Irr}^x(G)$, $\chi(1)_p=f(\chi)(1)_p$ and $\mathbb{Q}(f(\chi)(x))=\mathbb{Q}(\chi(x))$. This generalizes the picky conjecture: when $x$ is picky, the subnormalizer equals the normalizer of the unique Sylow $p$-subgroup containing $x$. The source records substantial results for this family of conjectures, but does not state that the general subnormalizer conjecture is solved.