ImageMagick with `-dither` and `-remap` could also work. For remap you would need an image with your desired palette, and IIRC you could use ImageMagick to prod

ImageMagick with `-dither` and `-remap` could also work. For remap you would need an image with your desired palette, and IIRC you could use ImageMagick to produce that image but I cannot recall the incantation required for that.