Greg Beetham wrote:... the ragged transitions that occur when downsizing the jpeg for the web, ...
No, Greg, that problem is fundamental.
First, all the gamma-emphasized formats with the 8bit colour must produce some posterisation on smooth colour transitions, especially in the brighter parts of the image where that gamma pre-emphasis makes digital levels too scarce.
Second comes the encoding of JPEG format, that is not RGB, it's Y-Cr-Cb; and that Y (luma) is only 8bit even before compression. Then the chroma Cr Cb are normally (4:2:2) encoded with half spatial bandwidth. And also the nature DCT JPEG compression is to discard small changes in the original value until the accumulated change becomes too large.
Now if you downsize for web, you not only overcompress causing banding in DCT, you also average out the noise that was originally providing some dithering that prevented posterisation.
So the only way to keep smooth colour transitions in overcompressed downsized JPEGs is to use dithering by adding noise to the original.