The conjecture that every uniform tree is good

Let $r\ge 2$, let $T$ be an $r$-uniform tree, and let $n$ be a positive integer. An $r$-uniform tree $T$ is $n$-good when its Ramsey number against the complete $r$-uniform hypergraph satisfies the corresponding goodness equality. The conjecture that every uniform tree is good. If $r\ge 2$ and $T$ is any $r$-uniform tree, then $T$ is $n$-good.

This is stated as a stronger version of the preceding conjecture and would imply that all $r$-uniform trees attain the expected Ramsey bound for every $n$. The source gives no resolution, while noting that the work already establishes infinitely many examples of $3$-uniform trees that are $n$-good.