Conjecture on universal invariants of bottom tangles concordant to boundary tangles

Set $v=\exp\frac{h}{2}$ and $q=v^2$, and let $J_T$ denote the universal $sl_2$ invariant of a bottom tangle. Let $(\bar U_q^{ev})\;\hat {}^{\;\hat \otimes n}$ be the subalgebra introduced in the paper, contained in $(\bar U_q^{ev})\;\tilde {}^{\;\tilde \otimes n}$. An $n$-component bottom tangle is concordant to a boundary bottom tangle if it is concordant to such a tangle; in particular, every slice bottom tangle has this property. Conjecture on concordance and integrality. If an $n$-component bottom tangle $T$ is concordant to a boundary bottom tangle, then

$$J_T\in (\bar U_q^{ev})\;\hat {}^{\;\hat \otimes n}.$$

The claim generalizes Habiro's boundary-bottom-tangle conjecture and the paper's theorem for ribbon bottom tangles. The supplied text does not state whether this generalization is resolved.