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We present moderate-resolution spectroscopy of extraplanar diffuse ionized gas (EDIG) emission in the edge-on spiral galaxy NGC 4302. The spectra were obtained with the SparsePak integral field unit (IFU) at the WIYN Observatory. The wavelength coverage of the observations includes the [N II] λ6548, 6583, Hα, and [S II] λ6716, 6731 emission lines. The spatial coverage of the IFU includes the entirety of the EDIG emission noted in previous imaging studies of this galaxy. The spectra are used to construct position-velocity (PV) diagrams at several ranges of heights above the midplane. Azimuthal velocities are directly extracted from the PV diagrams using the envelope-tracing method and indicate an extremely steep drop-off in rotational velocity with increasing height, with magnitude ~30 km/s/kpc. We find evidence for a radial variation in the velocity gradient on the receding side. We have also performed artificial observations of galaxy models in an attempt to match the PV diagrams. The results of a statistical analysis also favor a gradient of ~30 km/s/kpc. We compare these results with an entirely ballistic model of disk-halo flow and find a strong dichotomy between the observed kinematics and those predicted by the model. The disagreement is worse than we have found for other galaxies in previous studies. The conclusions of this paper are compared to results for two other galaxies, NGC 5775 and NGC 891. We find that the vertical gradient in rotation speed, per unit EDIG scale height, for all three galaxies is consistent with a constant magnitude (within the errors) of approximately 15-25 km/s per scale height, independent of radius. This relationship is also true within the galaxy NGC 4302. We also discuss how the gradient depends on the distribution and morphology of the EDIG and the star formation rates of the galaxies, and consequences for the origin of the gas.