Projective-flatness conjecture for vector bundles of radial Kupka components

Let $M$ be an algebraic manifold with $\dim_{\mathbb{C}}M\geq3$, let $L$ be a very ample line bundle on $M$, and let $\omega\in K(M,L,x\,dy-y\,dx)$ be a foliation with normal bundle $L$ and a compact, connected radial Kupka component. Let $V$ be the associated rank-two holomorphic vector bundle, arising from an exact sequence $0\longrightarrow\mathcal{O}\longrightarrow V\longrightarrow\mathcal{J}_{K}(L)\longrightarrow0$. Projective-flatness conjecture. The vector bundle $V$ is projectively flat. In the positive-line-bundle setting such a bundle exists and has total Chern class $c(V)=\left(1+\frac{c_1(L)}{2}\right)^2$, but it need not be semistable in general; projective flatness is posed as the remaining general-case property.