Found it. In ImageReady, it's all about "optimization". First, use the Color Table palette (Window > Color Table) to create the 4 color empeg palette described above.

Open the Optimization palette (Window > Optimize). Tell it to use the Custom color table whose dropdown should show 4 colors. NOW you can change the dither method and the % amount of dither.

Then the magic happens: 4-up view, showing original and three different dithers at once. Click View then Show Optimized, then again click View and Show 2-Up. Click a view and set its dithering options in the Optimization palette (ie: view 2 uses Diffusion, view 3 uses Pattern, view 4 uses Noise; or view 2 has 100% dither, view 3 has 85% dither, and view 4 has 70% dither).

Adjust brightness and contrast to modify how the empeg-optimized image, using hilights and shadows to show the most detail with those few colors. Keep trying different dither methods and percentages until one looks good. The method can make the 4 color result look quite different.

When finished, click File then Save Optimized As. That gives you an animated GIF (and if you don't know how to create the animation part to begin with, well I don't really either; I just keep inserting layers and frames, then showing a different layer in each frame). Done.