Matching-divisors conjecture for regular quotients and symplectic Pfaffians

Let $X=G/H$ be an affine homogeneous spherical variety with abelian regular centralizers and no type $N$ roots. Let $\mathfrak c=(\mathfrak h^\perp){/\!/}H\simeq\mathfrak c_{G_X^\vee}$, let $\mathfrak D_{ns}\subset\mathfrak c$ be the divisor over which the regular quotient generically has two preimages, and let $\mathfrak D\subset\mathfrak c_{G_X^\vee}$ be the divisor defined by the vanishing of $\mathrm{Pf}_X$. Matching-divisors conjecture. Under the natural identification $\mathfrak c\simeq\mathfrak c_{G_X^\vee}$, the divisors $\mathfrak D_{ns}$ and $\mathfrak D$ match exactly. This statement is presented as equivalent to the relative duality conjecture under additional hypotheses, including the regular-centralizer duality conjecture; it is not proved in general.