The weak polynomial degree conjecture for homology of elementary matrix groups

Let $I$ be a nonunital ring, let $I_+=I\oplus\mathbb{Z}$ be its unitalization, and let $\Gamma_I$ denote the corresponding functor from finitely generated free abelian groups to groups whose homology defines the functor $H_n(\Gamma_I)$. A functor is weakly polynomial of degree at most $d$ when it has weak polynomial degree bounded by $d$ in the sense used in the paper.

Weak polynomial degree conjecture. For every nonunital ring $I$ and every integer $n\in\mathbb{N}$, the functor $H_n(\Gamma_I)$ is weakly polynomial of degree at most $2n$.

This conjecture aims to recover and generalize Suslin's result that, under suitable vanishing and nonvanishing conditions on $\operatorname{Tor}^{I_+}_i(\mathbb{Z},\mathbb{Z})$, the functor $H_n(\Gamma_I)$ has weak polynomial degree $2$.