Turns out the problem was with the GOG update process itself. On a hunch, I just did a complete reinstall and the problem was fixed. Strange, as I had never missed a GOG update for Pillars.
I think the problem is that it wouldn't let me install patch 3.0 for vanilla PoE...it only let me install patch 3.0 for white march part I, and only after that point could I install white march part II. My guess is that the vanilla patch 3.0 update contained assets that weren't in the 3.0 update for white march part one, and that created the graphical glitches.
Short of the matter is, unless GOG fixes the patch files so you CAN install both the 3.0 update and white march 1 updates, the only fix is to do a clean install
You need to download both the vanilla AND the expansion version of the patch on GoG. I had this same issue the first time 2.0.1 was released, and when I installed both versions of the patch it solved the problem.
My guess is that most of the assets the patch needs to work are in one version, while the other makes further tweaks to be consistent with the expansion.