Nonreducibility of the universal treeable relation to Turing equivalence

Let $E_{\rm tree}$ denote the universal treeable countable Borel equivalence relation, and let $E_T$ denote Turing equivalence. A Borel reduction from $E_{\rm tree}$ to $E_T$ is a Borel function preserving and reflecting equivalence.

Treeable nonreducibility conjecture. The universal treeable countable Borel equivalence relation is not Borel reducible to Turing equivalence.

The conjecture is motivated by results showing that certain closure properties obstruct uniform reductions to equivalence relations generated by specified families of functions. Whether this nonreducibility holds is left open in the source.