We present results of a ground-based near-infrared campaign with Palomar TripleSpec, Keck NIRSPEC, and Gemini GNIRS to target two samples of reddened active galactic nucleus (AGN) candidates from the 31 deg$^2$ Stripe 82 X-ray survey. One sample, which is $sim$89% complete to $K<16$ (Vega), consists of eight confirmed AGNs, four of which were identified with our follow-up program, and is selected to have red $R-K$ colors ($>4$, Vega). The fainter sample ($K>17$, Vega) represents a pilot program to follow-up four sources from a parent sample of 34 that are not detected in the single-epoch SDSS catalog and have {it WISE} quasar colors. All twelve sources are broad-line AGNs (at least one permitted emission line has a FWHM exceeding 1300 km s$^{-1}$) and span a redshift range $0.59 < z < 2.5$. Half the ($R-K$)-selected AGNs have features in their spectra suggestive of outflows. When comparing these sources to a matched sample of blue Type 1 AGNs, we find the reddened AGNs are more distant ($z > 0.5$) and a greater percentage have high X-ray luminosities ($L_{rm X,full} > 10^{44}$ erg s$^{-1}$). Such outflows and high luminosities may be consistent with the paradigm that reddened broad-line AGNs represent a transitory phase in AGN evolution as described by the major merger model for black hole growth. Results from our pilot program demonstrate proof-of-concept that our selection technique is successful in discovering reddened quasars at $z > 1$ missed by optical surveys.
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