To implement the improvements you suggest on this site (which appears to be a static site), the best way would be to have your proposed image compression as part of the static site preprocessor, correct? Just trying to understand how it would be implemented, as this site is an interesting idea but the dithered images would likely not have mass-appeal.
Yes, you'd just run all of the images through jpeg-recompress (from the GitHub repo linked above). They're already doing something like this to dither, so it's just a question of swapping out which command to run.
Incidentally, even where PNG is appropriate (images with crisp edges, such as text and icons) you can frequently get a large size savings by applying zopflipng, which uses an alternative GZIP compression algorithm to get a higher-efficiency compression, at the cost of greater CPU use for encoding.[1]
