Dichotomy conjecture for idealistic Borel equivalence relations

Let $E$ be a Borel equivalence relation, and let $E_1$ denote eventual agreement on countable sequences of reals. Write $E\leq_B F$ when $E$ is Borel reducible to $F$. An orbit equivalence relation is induced by an action of a Polish group, and an idealistic equivalence relation is understood in the sense used in the paper. Dichotomy conjecture. Either $E_1\leq_B E$ or $E$ is Borel reducible to an orbit equivalence relation, or even just to an idealistic equivalence relation. This is a proposed dichotomy concerning idealistic equivalence relations. The source says that it remains unaffected by the results of the paper, but does not provide a resolution.