Intertwining operators between subregular Whittaker modules for ${\mathfrak{g}\mathfrak{l}}_N$ and non-standard quantizations

In this paper, we study intertwining operators between subregular Whittaker modules of ${\text{gl}}_N$ generalizing, on the one hand, the classical exchange construction of dynamical quantum groups, on the other hand, earlier results for principal W-algebras. We explicitly construct them using the generators of W-algebras introduced by Brundan-Kleshchev. We interpret the fusion on intertwining operators in terms of categorical actions and compute the semi-classical limit of the corresponding monoidal isomorphisms which turn out to depend on dynamical-like parameters.