Virtual reality (VR) and "metaverse" systems have recently seen a resurgence in interest and investment as major technology companies continue to enter the space. However, recent studies have demonstrated that the motion tracking "telemetry" data used by nearly all VR applications is as uniquely identifiable as a fingerprint scan, raising significant privacy concerns surrounding metaverse technologies. Although previous attempts have been made to anonymize VR motion data, we present in this paper a state-of-the-art VR identification model that can convincingly bypass known defensive countermeasures. We then propose a new "deep motion masking" approach that scalably facilitates the real-time anonymization of VR telemetry data. Through a large-scale user study (N=182), we demonstrate that our method is significantly more usable and private than existing VR anonymity systems.