It is possible that something cached is not routing your login request properly.
If you don't see the Develop menu in the Safari menu bar, choose Safari > Settings, click Advanced, then select “Show Develop menu in menu bar.”
Under the Safari Develop menu, select Empty Caches. Quit Safari. Now boot into Safe Mode (which you did already, but try it again). After doing that restart normally. Then see if the problem is gone.
My apologies if you already went through that with Apple ...
Also, did you try accessing that page from a new user account created just to test this?