The finite-colour Seurat game conjecture for digraphs

Let ${\bf G}^n(G,H)$ be the Seurat game with $n$ colours played on digraphs $G$ and $H$, with players $\forall$ and $\exists$, where $\forall$ seeks to distinguish non-isomorphic digraphs and $\exists$ seeks to match the colouring moves. Seurat game conjecture. There is $n\geq 2$ such that for all digraphs $G,H$, if $G\not\cong H$ then $\forall$ has a winning strategy in

$${\bf G}^n(G,H).$$

If true, this would say that a fixed finite number of colours suffices to distinguish every pair of non-isomorphic digraphs in these games; the source describes the question as open and notes that no pair of non-isomorphic graphs is known on which $\exists$ can avoid losing even with two colours.