Ahh, so it's definitely a thing, in person.
Does it change if you hit the degauss button (or select it from OSD options)?
You may have ambient magnetic fields messing up the beam path. Usually results in a much more noticeable rainbow effect, but Idunno.
Color convergence might also be a cause. The monitor probably has dynamic convergence (i.e., there's a beam-position-tweak signal, generated internally, that adjusts the beam as it scans across, mainly to account for the non-spherical shape of the screen), and if that's lagging for some reason, the picture will suffer.
Graphical Moire shouldn't appear for solid colors. It's normal for patterns, e.g. 50% gray, where the pixels won't quite line up with the pattern of phosphors on the screen (or the shadow mask / aperture grille).
There may be a Moire setting, though that may not be a good solution, either: AFAIK, the method used is shifting the entire display about a half pixel's distance, every frame. So the screen judders at half the refresh rate, like it's an interlaced display or something, except it's not. (The reason this can solve Moire: by shifting the screen half a pixel, the areas of pixels that were in the unlucky shadow areas pop out into view, while at the same time the areas that used to be bright, move into shadow; the average is hopefully a uniform picture. The flicker may be irritating, though.)
The pattern changing over time is interesting. Does it change quickly or slowly? If seconds to low minutes, it could be heating of electrical components, and something's out of spec and being sensitive. If slowly (mins to tens of mins), it could be thermal of something much bigger, like the CRT (and its aperture grille), or something that doesn't get hot by itself, but is heated by everything else getting hot, and doing the same thing.
Tim