Burr's universality conjecture for oriented trees

Let $n$ be a positive integer. An oriented tree is an orientation of a tree. A digraph is $n$-universal if it is contained in every $n$-chromatic digraph.

Burr's conjecture. Every oriented tree of order $n$ is $(2n-2)$-universal.

This is a generalization of Sumner's conjecture, which asserts that every oriented tree of order $n$ is contained in every tournament of order $2n-2$. The supplied text gives no evidence resolving Burr's stronger universality conjecture.