We can adjust the original 0-65 table to 6-bit 0-64 by subtracting one from all values > 32, which would give two 32 cutoff values. This would discard a 50% dither pattern from the center of the table, but the result would be much easier pixel value range scaling.
I suggest that we discard the pure 50% checkerboard, and use that as a "special" pattern created with different function. It LOOKS like pure gray because the pixels are too small to see with the naked eye. I have used 50% checkerboard gray in some of my buttons for drop shadows. It makes a nice addition or pure black and white for area fills, when you want to avoid that "looks bad in black and white" problem you can have with full dithering.
As I said all along, dithering is for the ANIMATED portions of the display, and the static portions can be full grayscale antialiased text and images. I think that this should be used in this VNC viewer too, with area motion detection for changing moving areas of the display content to dithered, leaving unchanging areas as full grayscale. By the way, on the touch, when I used my palpump demo using real gray byte values 0-255 instead of dithering, I only get 16 shades of gray (truncated values, not rounded, so only value 255 is white). That means the 8-bit colors are for ease of use, but are really still just 16-colors. You need to dither down from 256 to 16 colors to see a good image, so that must be what eips uses to display PNG images. I may need to adapt my dither function for dithering 256 colors down to 16-colors out of necessity for the touch.
