Vanishing conjecture for the congruence subgroup homology

Let $k$ be the field appearing in the power-series congruence subgroup, let $n,m$ be positive integers, let $p$ be a prime, and write $C_{n,m}(k[[t_1,t_2,\dots,t_m]])$ for the corresponding congruence subgroup. For every positive integer $l$, consider its homology with coefficients in $\mathbb Z/p$. Vanishing conjecture. For all $l>0$,

$$H_l(C_{n,m}(k[[t_1,t_2,\dots,t_m]]),\mathbb Z/p)=0.$$

If true, this would yield the displayed comparison of the homology of $SL_n$ over the power-series ring and over $k$; the source gives no resolution of the vanishing assertion.