Update:
I had another epiphany about this sort of animation.
In order to get assets to appear to be offset, you have to duplicate them on the texture and stretch them into an offset, as well as update the UV's.
The result is that you get one leaf showing up before the other, and moving twice as slow.
So in essence, you get different timing for each leaf using a single material and animation curve.
Did this with my vines to get this result as well.
Kinda neat!
The trick is to make sure you start the UV's all in the same place. I usually go to the last frame to set up the alignment.
The last thing you can do is non-uniformly modify the length of the mesh itself to get slightly offset timing. So scaling along the axis the texture is moving gives a slightly offset effect.
It helps if you're looking for that invisible variety that you get from editing something with your hands and not just letting the computer do everything for you.
