I've found a similar problem in Illustrator (which doesn't even have a "dither" option for gradients). It sounds a bit crazy, but I get around it by applying a "glass" filter, which can approximate dithering with the right params.
- Distortion: 2 (this is dependent on the side of your bands).
- Smoothness: 1
- Texture: Frosted (the noisiest built-in texture)
- Scaling: 50%
In Illustrator, this introduces white specks at the edges of your object, which you can fix by using a clipping mask.
Results? "Dithered" one on the right. It does add a bit of a noisy texture, but I think it's better than the bands most of the time.