I ended up fixing the problem on my own.
The issue was that Drastic and Retroarch were trying to render the resolution at 640W x 480H, which would cause squishing issues.
By adding in:
hdmi_cvt 480 640 60
Into the config.txt, I was able to give drastic another resolution to render at, solving the issue. For retroarch, I made the auto fullscreens resolution the 480W x 640H that the display was native to, which also solved the squishing.