The Weyl-monodromy realization conjecture for D and E singularities

Let $W$ be the Weyl group associated with a singularity of type $D_n$ or $E_n$. For some proper smooth surface $X/K$, consider an integral model of $X$ whose special fiber has a singularity of the specified type, and let the monodromy operator act on the relevant cohomology. Weyl-monodromy realization conjecture. One may construct an integral model of some proper smooth surface $X/K$ such that the monodromy operator lies in any conjugacy class of $W$. This is presented as a conjectural statement and is described as work in progress; the claimed realization of all Weyl-group conjugacy classes is not established in the source.