So I set video to 1920x1080 and with 30 fps I want to set shutter speed to 60. I find the only menu item labeled "shutter" and when I dial it down from where it currently was (800-1000) to 60, it blows out brilliant white. Obviously a bad thing. So do I have the right menu item or is this an ND filter thing? Being an engineer I am into things technical but this photography thing has escaped me over the decades.

"I want to set shutter speed to 60. I find the only menu item labeled "shutter" and when I dial it down from where it currently was (800-1000) to 60, it blows out brilliant white."

The problem here is that the lens is fairly fast (it lets a lot of light in - f2.8) and your average daylight scene would give a rough exposure value of 1/100th sec at f11 using ISO = 100.
Because you can't stop down the aperture and it stays wide open letting lots of light in, the correct exposure would be around 5 stops more than the setting you want.
That's why it's over exposed - it needs to have the light hitting the sensor reduced by about 5 stops if you want to use 1/60th with that lens in good daylight.