Symplectic-ball conjecture for Lagrangian products of a simplex and parallelohedra

Let $S$ be a three-dimensional simplex and let $P$ be any one of the five three-dimensional parallelohedra, namely the cube, hexagonal prism, elongated dodecahedron, rhombic dodecahedron, or truncated octahedron. Suppose that $S$ and $P$ are placed in an appropriate linear position, and denote their Lagrangian product by $S\star P$. Lagrangian-product symplectic-ball conjecture. The Lagrangian product $S\star P$ is symplectically equivalent to a Euclidean ball. This would generalize the question posed by Balitskiy concerning Lagrangian products of a simplex and a permutohedron, and would extend the paper's results on Lagrangian products and symplectic equivalence to further space-filling polytopes. The source presents this as a proposed generalization, with no resolution stated.