Bang-Jensen, Picasarri-Arrieta, and Yeo's characterization of champions

A tournament $H$ is a champion if there exists an integer $c_H$ such that every $H$-free tournament has acyclic dichromatic number at most $c_H$. The notation $TT_k$ denotes the transitive tournament on $k$ vertices, and $\Delta(1,1,k)\Rightarrow TT_k$ is interpreted using the tournament constructions defined in the source. Bang-Jensen, Picasarri-Arrieta, and Yeo's conjecture. A tournament $H$ is a champion if and only if $H$ is isomorphic to a subtournament of

$$TT_k \Rightarrow (\Delta(1,1,k) \Rightarrow TT_k)$$

for some integer $k\geq 1$. Since every champion is a hero but not every hero is a champion, this conjecture seeks a precise characterization of the tournaments whose exclusion gives a bounded acyclic dichromatic number.