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A recent analysis of the 100 pc white dwarf sample in the SDSS footprint demonstrated for the first time the existence of a well defined ultracool -- or IR-faint -- white dwarf sequence in the Hertzsprung-Russell diagram. Here we take advantage of this discovery to enlarge the IR-faint white dwarf sample threefold. We expand our selection to the entire Pan-STARRS survey footprint as well as the Montreal White Dwarf Database 100 pc sample, and identify 37 candidates with strong flux deficits in the optical. We present follow-up Gemini optical spectroscopy of 30 of these systems, and confirm all of them as IR-faint white dwarfs. We identify an additional set of 33 objects as candidates based on their colors and magnitudes. We present a detailed model atmosphere analysis of all 70 newly identified IR-faint white dwarfs together with 35 previously known objects reported in the literature. We discuss the physics of model atmospheres and show that the key physical ingredient missing in our previous generation of model atmospheres was the high-density correction to the He-minus free-free absorption coefficient. With new model atmospheres calculated for the purpose of this analysis, we now obtain significantly higher effective temperatures and larger stellar masses for these IR-faint white dwarfs than the Teff and M values reported in previous analyses, thus solving a two decade old problem. In particular, we identify in our sample a group of ultramassive white dwarfs in the Debye cooling phase with stellar parameters never measured before.