Hamiltonian classification conjecture for Lagrangian spheres in ADE Milnor fibers

Let $M$ be a surface Milnor fiber of an $ADE$-type singularity, with its standard zero sections and standard Lagrangian spheres. ADE Lagrangian-sphere conjecture. Every Lagrangian sphere in $M$ is Hamiltonian isotopic to one of the zero sections after applying a sequence of Dehn twists along these standard spheres. This conjecture is motivated by known descriptions of Lagrangian spheres in rational surfaces and symplectic mapping class groups of Milnor fibers. The source gives no resolution, so the claim remains open.