Conjecture that boundary Dehn twists have infinite order for general Seifert fillings

Let $Y$ be a negatively oriented Seifert-fibered $3$-manifold, let $\xi$ be a contact structure on $Y$, and let $(M,\omega)$ be a compact symplectic filling of $(Y,\xi)$ with $b^+(M)>0$. Denote by $\tau_M$ the boundary Dehn twist of $M$.

Boundary Dehn twist conjecture. The boundary Dehn twist $\tau_M$ has infinite order in the smooth mapping class group

$$\pi_0\bigl(\operatorname{Diff}(M,\partial M)\bigr).$$

This conjecture proposes removing the $S^1$-invariance assumption on the contact structure from the theorem established immediately beforehand. The theorem is known for negatively oriented Seifert-fibered rational homology $3$-spheres with $S^1$-invariant contact structures; the general case remains open.