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The ALFALFA blind extragalactic survey has populated the faint end of the neutral hydrogen (HI) mass function with statistical confidence for the first time. Of particular interest is a subset of the ALFALFA detections, termed "ultra-compact high-velocity clouds" (UCHVCs). These systems, if located within ~1 Mpc, would populate the lowest-mass end of the HI mass function. Subsequent optical imaging has revealed that some of these UCHVCs harbor associated (though sparse) stellar populations, revealing that they may be some of the most extreme galaxies known in the Local Volume, with optical properties akin to ultra-faint dwarf galaxies but with significant neutral gas reservoirs. In this campaign, we investigate the neutral hydrogen properties of six UCHVC candidate galaxies using deep VLA HI spectral line imaging. A companion poster (Paine et al.) presents details on the data reduction, imaging, and resulting products. Here, we examine the morphological and kinematic properties of selected sources. We apply the modeling software 3D-Barolo to our deep HI images in order to derive the rotation curve and constrain the inclination angle for each source. Successful modeling allows us to determine the dynamical masses of these objects and thus to consider them in the context of various fundamental scaling relations defined by more massive galaxies.