Oh, okay, turns out the horribleness is *NOT* directly related to dithering, but it's the (usual) Kindle's inability to deal with 16c PNGs properly.
If I apply the same workarounds as in the ScreenSavers hack (i.e., making it a 256c Gray PNG8 via
-define png:color-type=0 -define png:bit-depth=8), it behaves just fine, and the dithering pass doesn't mangle my own dithering

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Code:
Colors: 16
Histogram:
11815: (0,0,0) #000000 gray(0)
7995: (4369,4369,4369) #111111 gray(17)
5601: (8738,8738,8738) #222222 gray(34)
10304: (13107,13107,13107) #333333 gray(51)
12262: (17476,17476,17476) #444444 gray(68)
78117: (21845,21845,21845) #555555 gray(85)
91491: (26214,26214,26214) #666666 gray(102)
98963: (30583,30583,30583) #777777 gray(119)
109778: (34952,34952,34952) #888888 gray(136)
51459: (39321,39321,39321) #999999 gray(153)
43618: (43690,43690,43690) #AAAAAA gray(170)
47427: (48059,48059,48059) #BBBBBB gray(187)
55048: (52428,52428,52428) #CCCCCC gray(204)
59253: (56797,56797,56797) #DDDDDD gray(221)
65299: (61166,61166,61166) #EEEEEE gray(238)
27762: (65535,65535,65535) #FFFFFF gray(255)
The only downside to this workaround is larger filesizes.
FWIW, when I mention "my usual pipeline", it's this:
https://www.mobileread.com/forums/sh...1&postcount=17
Which is essentially a souped-up version of what the ScreenSavers hack does in cover mode (but with fancier scaling via EWA eliptical algorithms in linear space).
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TL;DR: Kindles are (probably) Doing It Right (mostly), which we kind of knew already, and isn't much of a surprise

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