Well I ordered the screen, it sat around for a month or more, and installed it eventually.... but it didn't solve the problem. So I ordered a DS90CF364AMTD, the IC that does the LVDS to LVTTL translation on the board with the power switch and LED in the front, and swapped in the new one.... same issue.
It looks like the glitch I'm seeing is actually part of the signal coming from the processor board itself, so while I don't expect to replace it, if I find one for cheap I may swap it and see if it makes a difference. The form factor is standard, so I'm sure there are options, but since the OS is a cut down windows XP, it probably only includes the drivers for the board being used, and it may be a real pain getting it to work with a different CPU module. I don't have a differential probe and don't really have experience probing LVDS, so at the moment I am not trying to figure out if there's some issue with that signal.
Though it occured to me a while back, the error I'm seeing has an interesting quirk: when there's enough green intensity in a row (think average green level), then the whole row's colors come right. When the green value is very high, the green value for the pixel is fine. When the row doesn't have a lot of green and the pixel doesn't have a lot, it doesn't work. You can see it in the bands of good color that appear in rows with a lot of bright colors (yellow in this pic), but I wonder if something like swapping the color palate of the window to something bright would actually improve overall color because of this quirk.
For now, at least, this will go unrepaired. I'll post again if I find a cheap CPU module replacement to test. I don't believe there's another chip off the CPU board that touches this LVDS signal.