resizing an image without constraining proportions will always result in a distorted looking image, could you not crop the square image into a rectangle and only use part of the image?
Or, shrink the square image so that it fits the height constraint of the rectangle then pad it out with something else? Another image? A feather gradient?
Unless you have a graphics package that has a built in magic tool for scaling images without distortion I don't think theres much else you can do.