We present analysis of the plateau and late-time phase properties of a sample of 39 Type II supernovae (SNe II) that show narrow, transient, high-ionization emission lines (i.e., "IIn-like") in their early-time spectra from interaction with confined, dense circumstellar material (CSM). Originally presented by Jacobson-Gal\'an et al 2024a, this sample also includes multicolor light curves and spectra extending to late-time phases of 35 SNe with no evidence for IIn-like features at <2 days after first light. We measure photospheric phase light-curve properties for the distance-corrected sample and find that SNe II with IIn-like features have significantly higher luminosities and decline rates at +50 days than the comparison sample, which could be connected to inflated progenitor radii, lower ejecta mass, and/or persistent CSM interaction. However, we find no statistical evidence that the measured plateau durations and $^{56}$Ni masses of SNe II with and without IIn-like features arise from different distributions. We estimate progenitor zero-age main sequence (ZAMS) masses for all SNe with nebular spectroscopy through spectral model comparisons and find that most objects, both with and without IIn-like features, are consistent with progenitor masses <12.5 M$_{\odot}$. Combining progenitor ZAMS masses with CSM densities inferred from early-time spectra suggests multiple channels for enhanced mass loss in the final years before core collapse such as a convection-driven chromosphere or binary interaction. Finally, we find spectroscopic evidence for ongoing ejecta-CSM interaction at radii $>10^{16}$ cm, consistent with substantial progenitor mass-loss rates of $\sim 10^{-4}$--$10^{-5}$ M$_{\odot}$ yr$^{-1}$ ($v_w < 50$ km/s) in the final centuries to millennia before explosion.
Comment: 30 pages, 20 figures, submitted to ApJ