Folk conjecture for tangent developable surfaces

Let $C\subseteq \mathbf{P}^{g-1}$ be a smooth canonical curve and let $T$ be its tangent developable surface in $\mathbf{P}^g$:

$$T=\operatorname{Tan}(C)\subseteq \mathbf{P}^g.$$

Folk conjecture. The tangent developable surface $T$ satisfies Property $(N_p)$ for

$$p=\left\lfloor\frac{g-3}{2}\right\rfloor.$$

The conjecture concerns the syzygies of tangent developables and is motivated by their cuspidal rational hyperplane sections, which degenerate canonical curves; the supplied text presents a proof via Koszul modules, so the conjecture is treated as solved.