Access by IP address - This made no difference, as the server automatically redirects me to the hostname version of the URL.
I was using Chrome, so I tried two other browsers: Edge and Firefox.
1. Edge 41.16299.15.0 fails to even load the admin page with the error "Too many redirects" (Error Code: INET_E_REDIRECT_FAILED). Same result in InPrivate mode.
2. Firefox 57.0 (64-bit) worked perfectly first time.
3. Chrome 62.0.3202.94 (Official Build) (64-bit) had the same issue, but when I dropped into an incognito window it worked just fine.
What on earth is happening here with these aggressive redirect loops being caused by session data (and not working at all in Edge)?