The top-degree cohomology conjecture for p-adic tame Tate twists

Let $A$ be a discrete valuation ring with local parameter $\pi$, perfect residue field $k$ of characteristic $p>0$, and fraction field $K$ of characteristic zero. Let $S=\operatorname{Spec}(A)$, let $X=\operatorname{Spec}(B)$ be a smooth $S$-scheme, let $I=(\pi)$ define the special fibre, let $B^h$ be the henselisation of $B$ along $I$, and let $i:\operatorname{Spec}(B/I)\to\operatorname{Spec}(B^h)$ be the inclusion. Top-degree cohomology conjecture. The object $R\epsilon_*i^*\mathcal T_r^t(n)\in D((\operatorname{Spec}(B/I))_{\mathrm{Nis}},\mathbb Z/p^r)$ is concentrated in degrees $[0,n+1]$, and there is an isomorphism

$$H^{n+1}(\operatorname{Spec}(B^h),\mathcal T_r^t(n))\cong H^1(\operatorname{Spec}(B/I),W_r\Omega_{\log,t}^n).$$

This is listed among the open problems for $p$-adic tame Tate twists. The source gives no proof or resolution.