No-singularity conjecture for embedded triod flow with positive length bounds

Let $\Omega\subset\mathbb R^2$ be a bounded, strictly convex domain, and let $\mathbb T_t$ be the flow by curvature of an embedded triod in $\Omega$. Assume that the lengths of the three curves are uniformly bounded below by a positive constant. No-singularity conjecture. The flow $\mathbb T_t$ does not develop singularities at all. This would follow from the translation conjecture for the relevant Type II blow-up limits and would establish global regularity under the stated lower length bound. The source gives no resolution of this conjecture.