The distribution of the very-high-energy diffuse emission in the inner 200 pc measured by H.E.S.S. indicates the existence of a pronounced cosmic-ray (CR) gradient peaking on the Galactic center (GC). Previous studies have shown that these data are consistent with a scenario in which the CRs are diffused away from a stationary source at the GC. We previously showed that, taking the 3D gas distribution and a realistic distribution of supernova explosions into account, CRs accelerated in supernova remnants should account for a large fraction of the GC CRs observed by H.E.S.S.; but the model did not fully reproduce the apparent over-density in the inner 30 pc. In this work, we study the time-energy dependent cosmic rays escape from the remnant that is expected to occur when the shock wave decelerates in the surrounding medium. We show that the resulting CR distribution follows the quasi-stationary profile observed by H.E.S.S. more closely. The main signature is that the energy-dependent escape creates a strong dependency of the morphology of the γ-ray emission with the energy. The existence of this energy dependency should be observable by the Cherenkov Telescope Array.