Additive realization conjecture for multiplicative hypertoric varieties

Let $\mathfrak{U}$ be a multiplicative hypertoric variety. An additive realization of $\mathfrak{U}$ consists of an additive hypertoric variety $\mathfrak{M}$, a divisor $\divisor\subset \mathfrak{M}$, and an isomorphism

$$\mathfrak{U} \cong \mathfrak{M}\setminus \divisor.$$

Additive realization conjecture. Every multiplicative hypertoric variety admits an additive realization: there exists an additive hypertoric variety $\mathfrak{M}$, a divisor $\divisor\subset \mathfrak{M}$, and an isomorphism

$$\mathfrak{U} \cong \mathfrak{M}\setminus \divisor.$$

This would identify multiplicative hypertoric varieties with complements of divisors in additive hypertoric varieties and explains the relation with the SYZ mirror construction for additive hypertoric varieties. The source presents this as a conjecture without resolving it.