The issue with planes has been fixed! Well..... a workaround has been discovered!
Basically, what it boils down to is a glitch in how the plane aligns the UV texture (see below)
The two planes use the same texture, same scaling and texture angle, and the planes are in the exact same spot/rotation on the map for convenience sake. I omitted the extraneous details such as ID, plane name, material file, etc for easier reading. You can see the edges of the UV textures line up with different corners on the broken plane than they do on the normal one. I don't think different numbers are a problem, but having negatives instead of positives probably is.
For anyone else dealing with this incredibly annoying thing, I'm so sorry. The solution's not a quick fix
1 - Select your entire map and export it. The whole thing. Don't group it first, the grouping thing gets super glitchy with large numbers of objects (or if you press ctrl+z too many times)!
2 - Create a new map in HPL2, check whether your plane texture works there
3 - If yes, WOOHOO!
3.5 - If no, start a new document immediately and repeat these steps.
4 - Import your map, use the uncontaminated plane you created in step 2 to start replacing the contaminated ones
5 - Celebrate your victory over this nightmare glitch