Arias's degree-one defect classification conjecture

Let $u$ be a congruence class modulo $3$, let $1\leq\alpha<\omega^\omega$, and let $q$ be a stable number with

$$\delta(q)=\mathscr{D}^{u}_{\mathrm{st}}[\alpha].$$

Define

$$A:=\{\mathscr{D}^{u+1}_{\mathrm{st}}[\omega\alpha+k]:k\in\mathbb{Z}_{\geq0}\}$$

and

$$E:=\{\delta_{\mathrm{st}}(b(a3^k+1)):k\geq0,\ ab=q\}.$$

Arias's conjecture. The set $A$ has finite symmetric difference with $E$, and the one-sided difference $A\setminus E$ is a finite subset of

$$\{\delta_{\mathrm{st}}(2^k):k\in\mathbb{N}\}.$$

The surrounding text identifies this as one of Arias's Conjectures 9--11; the supplied status information does not indicate a resolution.