The smoothness conjecture for the EKOR zip stack

Let $ocG_K$ be the parahoric group scheme, let $oM_K$ be the corresponding local-model stack, and let $EKORZip$ be the EKOR zip stack. The natural morphism to the quotient stack is

$$EKORZip\longrightarrow [ocG_K\backslashoM_K].$$

Smoothness conjecture. The morphism

$$ocG_K\text{-EKORZip}\longrightarrow [ocG_K\backslashoM_K]$$

is smooth.

The question arises because the reduced fibers of the EKOR zip stack over the local-model quotient are understood, but it is not known whether the fibers themselves are reduced; smoothness would provide the desired geometric control for the map from the Shimura variety to the EKOR zip stack.