Magnonic neural networks require compact resonant nodes that scatter spin waves efficiently, concentrate spin-wave energy and can be reconfigured. Hybrid magnonic Fabry-Pérot resonators, formed by a ferromagnetic-metal stripe dipolar-coupled to a yttrium iron garnet (YIG) film, provide low-loss and programmable control of spin-wave transmission, but have so far been studied only for stripes that are long compared with the spin-wave wavelength. Here we use micromagnetic simulations to determine how the response of a 200-nm-wide CoFeB stripe on a 55-nm-thick YIG film evolves as the stripe length is reduced from infinity to 640 nm. An infinitely long stripe acts as a one-dimensional cavity that opens a transmission gap at the first-order resonance (1.70 GHz and 1.47 GHz for the parallel and antiparallel magnetic configuration) and enhances the out-of-plane precession amplitude in the YIG film by factors of about 5 and 12, without distorting the transmitted wavefront. For lengths of a few micrometers, backward-volume spin waves emitted from the stripe ends modulate the precession along the stripe and fragment the reflected and transmitted wavefronts. Below about 1.2 micrometer, the resonator scatters incident spin waves over the entire isofrequency contour of the film, with caustic beams that are most pronounced in the antiparallel configuration. In this regime the parallel configuration supports weakly enhanced quantized modes, whereas the antiparallel configuration supports a single mode with an out-of-plane enhancement of about 15. The width, thickness and shape of the stripe tune this mode by 50-100 MHz, and its strong enhancement lowers the onset of nonlinear frequency shift and fold-over to incident amplitudes of a few percent of the saturation magnetization. Sub-micrometer magnonic resonators are therefore promising reconfigurable nonlinear nodes for magnonic networks.