I wish I knew to post the following earlier...

Personally I would use Palette Suite to make eight (or however many) "minipalettes" and save each individual palette (.pal) file. In other words, I would edit the palette (such as seen in the second picture in the article) so the colors used for the animation get shifted similar to how the article describes. Then, with PSP (I use v7), I would load each palette file--with the Maintain indexes option selected--onto an image with the original palette. And this would be done to make seven seperate images in addition to the unedited original image. With some special palette work, you won't even have to remake the eight palette files for different animations.

This can also be done using TilesetPal instead, but I find PSP to be more straightforward. I think this method is faster than the one in the article, especially if you get the hang of rotating colors around in Palette Suite by doing two consecutive reverses of the color order (one with 8 colors selected, and the other with 7).