Ghehe, I can't help simultaneously feeling pity for you struggling with this and laughing
Forgive me
I can understand the logic you're following though.
You want to displace a surface so you need a displacement shader.
Check, you did that.
Now, this displacement shader wants a shader as input in order to create the displacement.
Creating another displacement shader one level below creates the exact same displacement shader which still needs that damn input.
And again and again...
What the displacement shader actually needs is colours and scalars as input for example.
You already have something as colour, your global image map.
So instead of creating a displacement shader you choose "new shader -> colour shader -> image map shader -> select your global image map"
Go to your image map shader and set the projection mode from "through camera" to "spherical".
Copy the coordinates from the planet-node into the coordinate input of the image map shader and your texture will be correctly spherical mapped.
The image map shader needs these coordinates in order to spherically map from a centre position, which is the planet you want to map on.
That should be it!
Cheers,
Martin