Well, I decided to drop in on a Saturday visit, and see there is lots of discussion going on.
First, if it matters to anyone, I am posting some more images. I forgot one factor in the equation of image comparisons -- the 16-shades images.
The same two images as in the post above, 1200px wide. Saved with the following settings:
16-shades indexed, saved to png. These will not display properly on many (all?) ADE-based reader, long-standing bug.
16-indexed,convert to 256-indexed, saved to png.
16-indexed, saved to 256 default greyscale png.
Reducing images to 16-shades is not useful for jpeg format.
A brief comparison test saving the same image to jpeg got me these results:
326 kb -- 16-shades indexed palette
319 kb -- 256-shades indexed palette
319 kb -- 16 million colors
306 kb -- 16-shades converted to 256-greyscale
299 kb -- 16 million colors converted to 256-greyscale
So if you must use jpeg, it would seem you get best result by going from 16-million-colors to 256-greyscale. (this information is probably on Wikipedia or somewhere, but I don't get out as much as I should

) But I also see that jpeg with more than about 5% compression always dirties up the file, spitting lots of gray pixels into the white, so all our "death-to-specks" efforts are gone for naught.
I am also attaching the source images, originally downloaded in jp2 format,
saved to 24-bit png, EDIT - NOPE, had to use the original jp2 files, png too large and won't upload ---] and the full-size cleaned images in 24-bit png. Maybe someone will see something useful to suggest.
@derangedhermit, I wonder if the aliasing you see might not be an inherent result of "cleaning" --- brightening up the background from dark sepia to white is going to lose some of the paler shades. If I use a blur or "softening" tool, the entire image starts to look too soft. I wonder how other folks cure that. I do see that all these images look pretty good in my editor --- Edit --AND IN SIGIL --, and as noted in my earlier post, rather poor in ADE, with aliasing and pixilation.
@Tex --- My PSP only offers the option to use "Web-Safe-Palette", which is an ugly palette indeed; it changes lots of the pixels to "nearest color", and mostly "nearest" is not nearly "near" enough

. The poor picture looks like it is suffering from smallpox.
The other related options are "Interlaced or Non-interlaced", "Transparency", and "Gamma". I have never messed with the gamma option, don't know if that would apply for use in ebooks? I guess I will give scriptpng another shot, but I don't know if anything will change much.