The material function vectortoradialvalue can actually generate that radial mask using UVs. I will load up the editor in a few hours and see what output you need to use.
As far as getting your texture version to work, is the gradient linear? If so go into the texture options and make sure you uncheck sRGB. That will make it linear, since sRGB makes things nonlinear. A more stable way to control the distance would be to add instead of multiply before flooring. Adding 0 would be 0%, 0.5 would be 50% etc.