Searching for Cool Dust: II. Infrared Imaging of the OH/IR Supergiants, NML Cyg, VX Sgr, S Per and the Normal Red Supergiants RS Per and T Per

New MMT/MIRAC (9-11 {\mu}m), SOFIA/FORCAST (11-37 {\mu}m), and Herschel/PACS (70 and 160 {\mu}m) infrared (IR) imaging and photometry is presented for three famous OH/IR red supergiants (NML Cyg, VX Sgr, and S Per) and two normal red supergiants (RS Per and T Per). We model the observed spectral energy distributions (SEDs) using radiative transfer code DUSTY. Azimuthal average profiles from the SOFIA/FORCAST imaging, in addition to dust mass distribution profiles from DUSTY, constrain the mass-loss histories of these supergiants. For all of our observed supergiants, the DUSTY models suggest that constant mass-loss rates do not produce enough dust to explain the observed infrared emission in the stars' SEDs. Combining our results with Shenoy et al. (2016) (Paper I) we find mixed results with some red supergiants showing evidence for variable and high mass-loss events while others have constant mass loss over the past few thousand years.