Aint that only an issue when talking of multiple instances on the same server?
Yes, that appears to only be important if they are hosted on the same server.
Seems not viable just to hit root URL for health probing as it redirects to location: login.
You should be able to just hit the login URL and check for a 2xx, if you hit the login URL and the server isn't ready, I think you'll get the 503 still.