Quaternionic quotient-field conjecture for slice-preserving semiregular functions

Let $D$ be a symmetric slice domain in the quaternions, and let $\mathcal{O}_s(D)$ denote the integral domain of slice-preserving regular functions on $D$, with quotient field $\mathcal{Q}(\mathcal{O}_s(D))$. Let $\mathcal{M}_s(D)$ denote the field of slice-preserving semiregular functions on $D$. Quotient-field conjecture.

$$\mathcal{Q}(\mathcal{O}_s(D))=\mathcal{M}_s(D)$$

for every symmetric slice domain $D$. The equality is known when $D=\mathbb{H}$ by the quaternionic analogue of the Weierstrass factorization theorem; the general case would follow from an analogue of that theorem for regular functions on symmetric slice domains.