Anton's corrected vanishing conjecture for $GL_2$

Let $p$ be a regular odd prime, let $\zeta_p$ be a primitive $p$th root of unity, set $R=\mathbb Z[\zeta_p,1/p]$, and let $k=\mathbb F_p$. Let $D_1(R)$ denote the diagonal subgroup of $GL_1(R)$. Anton's corrected conjecture. One should have

$$H_2(GL_2(R);k)\cong H_2(D_1(R);k).$$

This reformulation was proposed after counterexamples to Quillen's original surjectivity conjecture, but the supplied text does not state whether Anton's corrected conjecture is resolved.