Conjecture on strong quasipositivity and Morse-Smale characteristic foliations

Let $(Y,\xi)$ be a contact $3$-manifold and let a transverse link in $(Y,\xi)$ be given. A Seifert surface for the link has a Morse-Smale characteristic foliation with positive singular points when its characteristic foliation is Morse-Smale and all its singular points are positive. Strong quasipositivity conjecture. The transverse link is strongly quasipositive if and only if it has a Seifert surface whose characteristic foliation is Morse-Smale with positive singular points. This is proposed by analogy with the preceding characterization of Stein quasipositivity; the source gives no resolution, so the conjecture remains open.