Mulmuley's polyhedral conjecture for stretched plethysm coefficients

For partitions $\mu$, $\nu$, and $\lambda$, define the stretched plethysm generating function

$$\tilde{\mathsf{A}}_{\mu[\nu]}^\lambda(t) = \sum_{n\geqslant0} \mathsf{a}_{n\mu[\nu]}^{n\lambda} t^n.$$

Mulmuley's conjecture. The generating function $\tilde{\mathsf{A}}_{\mu[\nu]}^\lambda(t)$ is the Ehrhart series of a polytope.

Mulmuley conjectured this after rationality of the generating function had been proved. The supplied text states that Kahle and Michałek disproved the conjecture, so the asserted polyhedral realization does not hold in general.