Separate balance and poles conjecture for elliptic stable envelopes

Let $X$ be a smooth symplectic variety with finite $X^{\mathsf{T}}$, and suppose that the elliptic stable envelope exists. For $4\lambda,\mu\in X^{\mathsf{T}}$, define

$$s(a,z)=\dfrac{T_{\lambda,\mu}(a,z)}{\Theta(P_\mu)}=\dfrac{\left.\mathrm{Stab}^{Ell}_{X,\mathfrak{C},P}(\lambda)\right|_\mu}{\Theta(P_\mu)}.$$

Here $a$ and $z$ are respectively the equivariant and Kähler parameters, and properties 1), 2), and 3) refer to the properties that $s(a,z)$ is balanced in $a$, balanced in $z$, and has poles separately in $a$ and $z$, respectively. Separate balance and poles conjecture. The section $s(a,z)$ has properties 1), 2), and 3). In particular, its denominator may contain factors of the form $\vartheta(a)\vartheta(z)$ but not $\vartheta(az)$. These properties are known for hypertoric varieties and for quiver varieties with finite $X^{\mathsf{T}}$; the conjecture extends them to smooth symplectic varieties with finite fixed-point set whenever the elliptic stable envelope exists.