Subcanonicity conjecture for the Grothendieck topology of linear microbundles

Let $(\mathbf{Top},T)$ be the underlying site and let $(\mathbb{V},\mathcal{T})$ be the site obtained by augmenting it through the specified data $(\mathbf{Set},C,D,E,H)$. A Grothendieck topology is subcanonical when every representable presheaf is a sheaf. Subcanonicity conjecture. The Grothendieck topology $\mathcal{T}$ is subcanonical.

If true, this would considerably simplify the formulation of calculus in $\mathbb{V}$. The supplied source gives no resolution, so the conjecture remains open.