Did you ever get to the bottom of this? I have a similar setup as you with lots of models that have no UV information, but i want to use a tri-planar mapping (world aligned mapping), but have its projection aligned to the objects local pivot.
Ive followed some tutorials but none really seemed to give me what i was looking for… I tried plugging Object Local Pivot node into the WorldPosition input on WorldAlignedTexture but no joy…