The Airborne Infrared Spectrometer (AIR-Spec) offers an unprecedented opportunity to explore the near-infrared (NIR) wavelength range. It has been flown at two total solar eclipses, in 2017 and 2019. The wavelength range of the much-improved instrument on the second flight (2019 July 2) was shifted to cover two density-sensitive lines from S xi. In this paper we study detailed diagnostics for temperature, electron density, and elemental abundances by comparing results from AIR-Spec slit positions above the east and west limbs with those from Hinode/EIS, the PolarCam detector, and SDO/AIA. We find very good agreement in the electron densities obtained from the EIS EUV line ratios, those from the NIR S xi ratio, and those obtained from the polarized brightness PolarCam measurements. Electron densities ranged from log N e [cm−3] = 8.4 near the limb to 7.2 at R 0 = 1.3. EIS spectra indicate that the temperature distribution above the west limb is near isothermal at around 1.3 MK, while that on the east has an additional higher-T component. The AIR-Spec radiances in Si x and S xi, as well as the AIA data in the 171, 193, and 211 Å bands, are consistent with the EIS results. EIS and AIR-Spec data indicate that the sulfur abundance (relative to silicon) is photospheric in both regions, confirming our previous results of the 2017 eclipse. The AIA data also indicate that the absolute iron abundance is photospheric. Our analysis confirms the importance of the diagnostic potential of the NIR wavelength range and that this important wavelength range can be used reliably and independently to determine coronal plasma parameters.