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Hybrid integration of nanoplasmonic devices with silicon photonic circuits holds promise for a range of applications in on-chip sensing, field-enhanced and nonlinear spectroscopy, and integrated nanophotonic switches. Here, we demonstrate a new regime of photon-plasmon coupling by combining a silicon photonic resonator with plasmonic nanoantennas. Using principles from coherent perfect absorption, we make use of standing-wave light fields to maximize the photon-plasmon interaction strength. Precise placement of the broadband antennas with respect to the narrowband photonic racetrack modes results in controlled hybridization of only a subset of these modes. By combining antennas into groups of radiating dipoles with opposite phase, far-field scattering is effectively suppressed. We achieve ultrafast tuning of photon-plasmon hybridization including reconfigurable routing of the standing-wave input between two output ports. Hybrid photonic-plasmonic resonators provide conceptually new approaches for on-chip integrated nanophotonic devices.