In spite of the extensive studies of zero-index metamaterials, the realization of zero impedance with finite phase velocity has not been explored. Here, we show that this extreme case, realized by elaborately-tuned paired resonators, can effectively enhance sensing and actuation. To explain the formation mechanism of the near-zero effective impedance with finite phase velocity by paired resonators at a target frequency, a theory using an equivalent model based on mechanical longitudinal waves is developed. If the frequency of the extreme property is further tuned at a Fabry-Pérot resonance frequency, highly efficient enhancement is possible. Experiments using a piezoceramic transducer (PZT) installed on the plate region bounded by two resonators confirm that the proposed extreme property mechanism highly enhances the sensing and actuation outputs of the transducer.