The symmetry conjecture for tropical theta functions

Let $(X,E)$ be a smooth Looijenga pair with affine interior $U=X\setminus E$, let $u:\mathcal T\to X$ be the universal torsor, and set $G=\mathcal T|_U$. Let $V$ be the mirror to $G$, and let $\operatorname{Sk}(u)$ and $\operatorname{Sk}(V)$ denote the corresponding skeleta. For $u\in\operatorname{Sk}(u)$ and $v\in\operatorname{Sk}(V)$, write $\theta_{u\in\operatorname{Sk}(u)}^{\mathrm{trop}}(v)$ for the tropical theta function evaluated at $v$. Symmetry conjecture.

$$\theta_{u\in\operatorname{Sk}(u)}^{\mathrm{trop}}(v)=\theta_{v\in\operatorname{Sk}(V)}^{\mathrm{trop}}(u).$$

This is the proposed symmetry between the two tropical theta-function constructions and is part of the scheme intended to produce a theta-function basis of the Cox ring. The source gives no evidence resolving it.