Continuous variable quantum teleportation provides a path to the long-distance transmission of quantum states. Photon-varying non-Gaussian operations have been shown to improve the fidelity of quantum teleportation when integrated into the protocol. However, for a given type of non-Gaussian operation, the achievable fidelity varies with the parameters associated with the operation. Previous work only focused on particular settings of the parameters, over which an optimization was missing. The potential of such operations is not fully uncovered. Given a fixed non-Gaussian operation, the achieva...