Moving layers by half pixel (GIMP)
Increase (scale) the size of the entire image by 2 in both vertical and horizontal dimensions. This will result in an exact scale, where every single pixel in the original image is now four pixels (2x2) in the new image. Now shift the layer over 1 pixel, and then scale the entire image back down to the original size. Make sure the image supports anti-aliasing before down-scaling.
Additionally, having already scaled up, you may want to keep the higher resolution for any other edits until it's time to prepare the final version for publishing.