We present new constraints on the density profiles of dark matter (DM) halos in seven nearby, dwarf irregular galaxies from measurements of their integrated light stellar kinematics. Low mass galaxies are frequently observed by their gaseous kinematics to have constant density DM cores while N-body simulations instead predict a cuspy profile. This work builds on a pilot study where we found one galaxy, NGC 2976, to possess a cuspy DM halo when measured in the stars but a cored DM halo when measured in the gas. We now present an expanded data set of high resolution integral field spectroscopy on seven galaxies, with high enough S/N to measure the stellar and gas kinematics simultaneously. With these improved data, we explicate the cause of the discrepancy in NGC 2976 as triaxial structure that most strongly biases the modeling of the colder gas relative to the stars. We examine whether gas kinematics in general produce shallower density profiles than are derived from the stars. The larger sample shows that not all cores go away when measured with stellar kinematics and there remains a wide range of DM halo profiles between galaxies. Finally, we search for correlations of DM profile with disk structural properties, stellar velocity anisotropy and chemical abundances. Two popular mechanisms to explain cored DM halos are a warm DM component or feedback models which strongly couple the energy of supernovae into repeatedly driving out gas and dynamically heating the DM halos. We confront both models with our new constraints.