Stable ordered union ultrafilters and $\mathrm{c}\mathrm{o}\mathrm{v}(\mathcal{M})<\mathfrak{c}$

A union ultrafilter is an ultrafilter over the finite subsets of $\omega$ that has a base of sets of the form $\mathrm{F}\mathrm{U}(X)$, where $X$ is an infinite pairwise disjoint family and $$\mathrm{F}\mathrm{U}$(X)={\bigcup F\big|F\in[X]^{<\omega}\setminus{\varnothing}}$. The existence of these ultrafilters is not provable from the $\mathsf{Z}\mathsf{F}\mathsf{C}$ axioms, but is known to follow from the assumption that $\mathrm{c}\mathrm{o}\mathrm{v}(\mathcal{M})=\mathfrak{c}$. In this article we obtain various models of $\mathsf{Z}\mathsf{F}\mathsf{C}$ that satisfy the existence of union ultrafilters while at the same time $\mathrm{c}\mathrm{o}\mathrm{v}(\mathcal{M})<\mathfrak{c}$.