Removal of the technical condition for orientability of modules over local systems

Let $E_n$ denote the height-$n$ Morava $E$-theory spectrum, and let $\rho_{ ull}$ denote the $\rho$-localization functor. Write $\rho_{ ull}\bigl(\tau_{ ot< n}\bigl(\rho_{ ull}(\tau_{ ot< n}E_n)\bigr)\bigr)$ for the symmetric monoidal $\rho_{ ull}$-local category of modules over the category of $E_n$-local modules. Orientability conjecture. The $\rho_{ ull}$-local category of modules over the category of $E_n$-local modules is $(\mathbb{S}_{(p)},n+1)$-orientable:

$$\rho_{ ull}\bigl(\tau_{\not< n}\bigl(\rho_{ ull}(\tau_{\not< n}E_n)\bigr)\bigr) \text{ is } (\mathbb{S}_{(p)},n+1)\text{-orientable}.$$

This is the expected removal of the technical condition on the connective $(n+1)$-finite $p$-local spectrum in the preceding categorified orientation result; the source does not provide a resolution.