Universal-element conjecture for componentwise finite-minor graphs

Let $\mathcal F$ be the class of graphs $G$ such that no component of $G$ contains every finite graph as a minor. A graph $U$ is $<$-universal for a class if every graph in the class is a minor of $U$. Universal-element conjecture. The class $\mathcal F$ has a $<$-universal element. This would follow from the existence of $<$-universal elements for $\operatorname{Forb}(K_n)$ for every $n$; the source presents those cases as open for $5<n<\infty$, and proposes proving the assertion directly.