What you are referring to is SVM, or Scan Velocity Modulation. It is your TV attempting to create a more detailed picture by lightening the lights and darkening the darks at the border - a type of "edge enhancement". Unfortunately, this creates the "halo" effect that you refer to. Ironically, on most TVs, turning the sharpness all the way down usually turns SVM off. I've never heard of it being the opposite, as you have tried.
What model TV do you have? There's a chance, albeit a small one, that you might have a separate "SVM" switch that allows you to turn it off without affecting the regular sharpness control.