Is it necessary for peripheral movement to cease in order to realize the inner center, and how can this be achieved?

According to Osho, no: the periphery need not—and cannot—be made still. Nature is flux. Liberation comes not by stopping change but by disidentifying from it: witness the moving body-mind and reestablish awareness in the unmoving center. Allow everything to move without clinging or trying to fix it; sustained witnessing reveals ‘I am the stillness,’ so the world continues but not within you.