Perhaps I'm blind, but I don't see an option to 'copy the z-order across the entire animation.' I can paste to all key frames, but that's about it.
Also I'm sorry, I'll try to describe it better. I have an animation of a tent with a lot of key frames, used to make the tent sway as the player sleeps. I wanted to add a lantern outside of the tent that sways just a little in a soft breeze. It should be very easy to animate, using only a few key frames. The problem is, it seems like I need to animate the lantern for each existing key frame, which is considerably harder.