Update:

I finally got around to fixing the loose stab tube. Masking tape was too thick but Scotch tape was perfect. I was surprised by how much movement (in my eyes) was cured by Scotch tape being as it's so thin.

I also noticed whoever glued the tube into the right elevator half was kinda sloppy. The stab wouldn't sit flush against the fuse'. I filed the glue away and now it's a nicer fit. That in of itself might help to prevent the movement in the future.