The blur radius was calculated as a fraction of image resolution, while the blur sigma was left alone. This is completely incorrect. With ImageMagick, blur radius should be kept at 0, and blur sigma is measured in pixels (source). Sothe correct solution is to leave the radius at 0 and instead calculate the sigma as a fraction of image resolution.

Here's a decent comparison of analogous "before" (above) and "after" (below), taken from link above:

The box blur artifacts are significantly more noticeable in the "before", while the "after" is effectively indistinguishable from a Gaussian.