The generic sheaf quantizability conjecture for rotated holomorphic Lagrangians

Let $C$ be a Riemann surface and let $L\subset T^*C$ be a holomorphic Lagrangian. For a generic angle $\theta$, Solomon–Verbitsky theory places $e^{2\pi i\theta}\cdot L$ in the relevant Fukaya category. Generic sheaf quantizability conjecture. For generic $\theta$, the Lagrangian $e^{2\pi i\theta}\cdot L$ is sheaf quantizable. This follows conditionally from the conjectured Fukaya-to-sheaf embedding, and remains open in the generality stated.