Soare's effective automorphism conjecture for semilow sets

Let $A$ be a c.e. set. Its complement $\overline{A}$ is semilow when the corresponding semilowness property holds, and $A$ is low when $A'\equiv_T\mathbf{0}'$. Two c.e. sets are automorphic when an automorphism of the lattice $\mathcal{E}$ of c.e. sets maps one to the other. Soare's effective automorphism conjecture. Every semilow set is effectively automorphic to a low set. This would extend Epstein's result, which supplies a properly low$_2$ degree whose computable members are automorphic to low sets; the source gives no resolution of the conjecture.