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Theorem 5.1 in Recursively Enumerable Sets Modulo Iterated Jumps and Extensions of Arslanov's Completeness Criterion states that Arslanov's completeness criterion holds for $n$-REA sets. The paper is ...

Ohh, I think I was being dumb. There is a 2-REA operator $J$ such that $J(X) <_T X'$ isn't of degree r.e. in $X$. Since $0''$ is of r.e. degree in every $X < 0''$ with $X' \geq_T 0''$.