@derangedhermit -- Thank you so much for spending so much time on this. I do appreciate the good advice you're sharing.
I am going to search for Photoshop plugins, maybe they have something that is wonderful for healing aliasing. Otherwise, I guess I will use Gaussian blur, and see where that gets me.
I have been learning to use the histogram. The process of stretching the histogram is wonderfully easy, but my old version of PSP makes it difficult. The histogram window is really tiny, and I don't have wonderful vision anyway --- you need to move a slider to where the gap ends, and it is almost impossible for me to see that. Plus, the analysis is obtained by mousing over the histogram for a tooltip, and I find it really hard to select a specific shade. I think I will try to find a freeware tool that lets me do this with better visibility. Maybe I will have to go over to the dark side and really start using GIMP. Or maybe I will try out PSE
As far as the number of shades in the palette-- after desaturating and cleaning, that is all the shades that were left. I just confirmed by desaturating the source images again (desaturation=100%, light/dark level not used) :
--- 021 source file originally 91,288 colors, desat = 240 colors
--- 238 source file originally 195,232 colors, desat = 250 colors.
If I use my usual routine of Recoloring, it goes like this:
--- 021 = 91,288; recolored = 65,247; desat = 256
--- 0238 = 185,232; recolored = 91,106; desat = 256
I think cleaning would then remove some of those shades by lightening up some of the gray shades. As I have noted elsewhere, some PSP tools don't work unless you are in 16M colors, so I don't grayscale until the end.
I understand your wish for transparency. I don't know enough about support from various devices and software, but I think it is very spotty. I remember mention of at least one device (Kobo?) that displays png transparency as black! Very ungood. Possibly a more supportable (is that a word?) thing would be tinting the image background to a pastel color or pale gray. But that definitely is missing the cool factor!
In case you still would like a peek at the source files, I am attaching a zip of the two full-size images in JPEG. (I know, I know, saving as jpeg results in more degradation.) Used 1% compression, the closest PSP allows to zero for standard jpeg. The PNGS were quite large, and even though the zip at 17mb was under the upload limit of 20mb, the uploader kept timing out.