Output-polynomial enumeration for $2K_p$-free incomparability graphs

Let $p$ be a positive integer, let $2K_p$ be the disjoint union of two copies of the clique $K_p$, and let $\textsc{Dom-Enum}$ denote the problem of enumerating all minimal dominating sets of a graph.

The $2K_p$-free incomparability conjecture. For every $p$, there is an output-polynomial time algorithm for $\textsc{Dom-Enum}$ in $2K_p$-free incomparability graphs.

This is presented as a directly easier conjecture than the corresponding statement for incomparability graphs of $S_t$-free posets. It holds for $p=1$ and is known for $p=2$, while the case $p=3$ is widely open without the incomparability assumption.