Do you have some tips / links that could help me improve the dithering even further?
For my use case (a digital picture frame), I've simply rejected images that looked very bad after dithering, and that's very often
- (a) generally dark images,
- (b) very gradient-based images (banding appears) and
- (c) art with a color spectrum that's very narrow in lightness, but wide in value (i.e. most colors map to the same level of gray after converting to grayscale)
Besides using Floyd-Steinberg dithering, I have not tried anything fancy.
As I mentioned above, the exact quality of differing varies by a large amount depending on the tool. I would recommend comparing the quality of GIMP vs. other tools on a single example image.