Ramaswamy's conjecture on fail points

Let $\Omega$ be a planar convex domain symmetric about the two coordinate axes. A fail point is a point where $|\nabla u_{\Omega}|$ attains its maximum, where $u_{\Omega}$ is the torsion function. The largest inscribed circle is a circle of maximal radius contained in $\Omega$.

Ramaswamy's conjecture. The fail points occur either at the contact points of the largest inscribed circle or at points of minimal curvature.

This modified conjecture was proposed after Saint-Venant's conjecture was disproved and has been widely accepted in the mechanical engineering community. The source gives no resolution of Ramaswamy's conjecture.