Universally tight toric-annulus conjecture for adding Giroux torsion

Let $T$ be a convex incompressible torus in a tight contact 3-manifold $(Y,\xi)$ such that every toric annulus neighborhood of $T$ with convex boundary is universally tight. Conjecture. The contact 3-manifold obtained by adding Giroux torsion in a neighborhood of $T$ is tight.

This conjecture proposes a sufficient condition for adding Giroux torsion near an incompressible torus while preserving tightness. The surrounding discussion relates it to Honda's work and notes that the toric annulus neighborhoods must be universally tight, even though the ambient contact 3-manifold need not be universally tight.