There have been a few discussions here on noise projection ... might be useful for this.
The space is too big for noise projection I'm afraid, I would need several really strong flash guns.
My recollection is that Rhino works on color, not just brightness.
I've never had success using pieces of tape to add texture. Let us know how it works for you.
I will try Post-it notes with a random ink blob (stamped with a ball of crumpled paper). It seems this pattern generates a good amount of points. The edges or corners of the notes don't generate any points at all, so I can see why you didn't have good results with just tape.

(I will use yellow Post-its for more contrast)
Now the question is now many notes I need to put on my wall for a decent alignment.
I wish there was some paint that I could just splatter on and that disappears after a day. I know there exists wallpaper glue that is a light pink color when wet but completely transparent when dry.