I have tried the below solution twice now, with my existing trailhead playground and a new one.  Both show a red outline and wont let me add them.  How can I get this to work?

If you launch the Org from inside TrailHead you will get a URL like
https://random-words-123456-dev-ed.lightning.force.com/one/one.app#eyJjb21wb25lbnREZWYiOiJvbmU6YWxvaGFQYWdlIiwiYXR0cmlidXRlcyI6eyJhZGRyZXNzIjoiL2FwZXgvdGhfY29uX2FwcF9fVGhIb21lcGFnZSJ9fQ%3D%3D
 Take the random-words-123456-dev-ed.lightning.force.com and use that as your custom Org in the Login screen.
If you get a DNS error try creating a new Org.
To create a new Org in the TrailHead Module pull down the Org list beside the [Launch] button and select "Create TrailHead PlayGround"