Ah. Thank you so much for all that! I shall have to play with the Joint Editor. I had suspected it would be the answer but could not figure it out. Meanwhile, it also turns out that taking the prop into the Setup Room and turning it into a Figure *also* has the side effect of somehow resetting the origin as wish, with all the subparts showing up properly as belonging to the Figure. However, I'd rather have it be a simple prop, not a figure, so I'll definitely try playing around with the Joint Editor.

Thank you again.