We present a near-infrared spectroscopic survey of narrow-line Seyfert 1 galaxies in the southern hemisphere (using the SOFI instrument on the ESO-NTT telescope), sampled from optical surveys. We examine the kinematics of the broad-line region, probed by the emission line width of hydrogen (Paschen{alpha} and H{beta}). We observed 57 objects, of which we could firmly measure Paschen{alpha} in 49 cases. We find that a single Lorentzian fit (preferred on theoretical grounds) is preferred over multi-component Gaussian fits to the line profiles; a lack of narrow-line region emission, overwhelmed by the pole-on view of the broad line region (BLR) light, supports this. We recompute the catalog black hole (BH) mass estimates, using the values of FWHM and luminosity of H{beta}, both from catalog values and re-fitted Lorentzian values. We find a relationship slope greater than unity compared to the catalog values. We ascribe this to contamination by galactic light or difficulties with line flux measurements. However, the comparison of masses computed by the fitted Lorentzian and Gaussian measurements show a slope close to unity. Comparing the BH masses estimated from both Paschen{alpha} and H{beta}, the line widths and fluxes shows deviations from expected; in general, however, the computed BH masses are comparable. We posit a scenario where an intermixture of dusty and dust-free clouds (or alternately a structured atmosphere) differentially absorbs the line radiation of the BLR, due to dust absorption and hydrogen bound-free absorption.