Parallax websites are actually easy, because images are divided into many sprites/layers, so there's many palettes to work with.

I've got a pretty large collection of PNGs to test quantisation on and 68% of them end up converted in great quality, 89% are within acceptable range. It's about double of what you can get with Fireworks.

And for images that can't absolutely fit in 256-colors there's a hack for lossy true-color PNGs that can reduce size by 20-40%: https://github.com/pornel/mediancut-posterizer