Finiteness conjecture for extendable automorphisms of embedded tori

Let $T^p$ be a $p$-dimensional torus embedded in $S^{p+2}$. Consider extendable homeomorphisms of the embedding, and distinguish their mapping classes in $\operatorname{MCG}(T^p)$ from their linear mapping classes in $\operatorname{SL}(p,\mathbb{Z})$. Higher-dimensional torus finiteness conjecture. There is some $T^p$ embedded in $S^{p+2}$ such that it has finitely many mapping classes in $\operatorname{MCG}(T^p)$ or linear mapping classes in $\operatorname{SL}(p,\mathbb{Z})$ of extendable homeomorphisms. This is posed as a possible higher-dimensional analogue of the preceding surface question; the source gives no resolution.