Isomorphism conjecture for three deformed W-algebras of type $A_{2N}^{(2)}$

Let ${\mathcal W}_{x,r}\big(A_{2N}^{(2)}\big)$, ${\mathcal W}_{x,r}^{\rm AKOS}\big(A_{2N}^{(2)}\big)$, and ${\mathcal W}_{x,r}^{\rm FR}\big(A_{2N}^{(2)}\big)$ be the three deformed $W$-algebras associated with the twisted affine Lie algebra of type $A_{2N}^{(2)}$. The algebra ${\mathcal W}_{x,r}^{\rm AKOS}\big(A_{2N}^{(2)}\big)$ is defined as the projective limit of the quotients of the associative algebra generated by the modes $T_i[m]$ by the left ideals generated by sufficiently high modes.

Isomorphism conjecture. The three algebras are isomorphic as associative algebras:

$${\mathcal W}_{x,r}\big(A_{2N}^{(2)}\big)\cong {\mathcal W}_{x,r}^{\rm AKOS}\big(A_{2N}^{(2)}\big)\cong {\mathcal W}_{x,r}^{\rm FR}\big(A_{2N}^{(2)}\big).$$

The claim would identify the generator-and-relation, AKOS, and FR constructions of the deformed $W$-algebra. The supplied text does not state whether this conjecture has been proved or disproved.