We present results from the analysis of WIYN pODI imaging of 23 ultracompact high-velocity clouds (UCHVCs), which were identified in the ALFALFA H I survey as possible dwarf galaxies in or near the Local Group. To search for a resolved stellar population associated with the H I gas in these objects, we carried out a series of steps designed to identify stellar overdensities in our optical images. We identify five objects that are likely stellar counterparts to the UCHVCs, at distances of similar to 350 kpc to similar to 1.6 Mpc. Two of the counterparts were already described in Janesh et al.; the estimated distance and detection significance for one of them changed in the final analysis of the full pODI data set. At their estimated distances, the detected objects have H I masses from 2 x 10(4) to 3 x 10(6)M(circle dot), M-V from -1.4 to -7.1, and stellar masses from 4 x 10(2) to 4 x 10(5)M(circle dot). None of the objects shows evidence of a young stellar population. Their properties would make the UCHVCs some of the most extreme objects in and around the Local Group, comparable to ultrafaint dwarf galaxies in their stellar populations, but with significant gas content. Such objects probe the extreme end of the galaxy mass function and provide a test bed for theories regarding the baryonic feedback processes that impact star formation and galaxy evolution in this low-mass regime.