Regular-quotient gluing conjecture for spherical varieties

Let $X=G/H$ be an affine homogeneous spherical variety with abelian regular centralizers and no type $N$ roots. Let $\mathfrak c=(\mathfrak h^\perp){/\!/}H$, let $(\mathfrak h^\perp)^\mathrm{reg}\mathbin{\mkern-6mu\fatslash}H$ be the regular quotient, and let $\mathfrak D_{ns}\subset\mathfrak c$ be a divisor. Regular-quotient gluing conjecture. Away from a codimension $2$ locus in $\mathfrak c$, there is an identification

$$(\mathfrak h^\perp)^\mathrm{reg}\mathbin{\mkern-6mu\fatslash}H\simeq \mathfrak c\coprod_{\mathfrak c\setminus\mathfrak D_{ns}}\mathfrak c.$$

Thus the regular quotient is expected to be obtained by gluing two copies of the GIT quotient along the complement of a divisor. The paper says that this is verified in several examples, but does not establish it in general.