Global null control of a two-phase Stefan interface with signed initial temperatures

We prove that two Dirichlet boundary controls can drive a one-dimensional two-phase Stefan system to zero temperature and any prescribed interior interface position in every positive time. The initial temperatures may be arbitrary real smooth functions compactly supported in their phases, and the interface remains strictly inside the rod throughout. A short uncontrolled evolution gives analytic interface traces without a sign assumption. These traces are then extended by Gevrey interpolation and the flatness series of Colle, Lohéac and Takahashi, while a convex interpolation of the interface position prevents collision with the endpoints.