Can't access admin login page (redirect error)

Hello interwebs,

I’m working on a wordpress site, it’s almost finished.
Left it lying on the server for a few weeks after the launch to gather user feedback, and now ready to make some minute adjustments.
Loe and behold, can’t login.
Going to parentsauxassembleesgenerales.org/wp-admin won’t show me the admin page, but will instead redirect.
Sure enough, I had an automatic update to 3.8.2 on April 9 that seems to coincide with the admin access being gone.
Contrary to most redirect errors for login pages after an automatic update on forums, the exact url it redirects to is not actually a valid url.
You see others reporting the url they are redirected to as being:
http://www.domain.org/wp-login.php/?redirect_to=http%3A%2F%2Fwww.domain.org%2Fwp-admin%2F&reauth=1

But mine displays: http://www.parentsauxassembleesgenerales.org-login.php/?redirect_to=http%3A%2F%2Fwww.parentsauxassembleesgenerales.org%2Fwp-admin%2F&reauth=1

And is therefore missing three characters: “/wp” to be identical to the other bugs I saw reported. Needless to say, I still tried all the fixes recommended elsewhere, namely:

(using FTP, Softaculous, dowload of WP 3.8.1 and 3.8.2 from wordpress.org, and PHPmyAdmin)

1- deactivating, renaming, removing plugins, theme, both plugins and theme
2- adding lines of code to wp-config
3- looking at the database to make sure the site url and home url were the right ones and the same
4- updating key files like wp-login.php with a fresh version straight out of a vanilla install.
5- moving the content and wp-config to a fresh install (only recreated the problem).

I’m sort of confused at Softaculous (wp install script in cPanel) for asking if you want automatic updates, but still enabling the small automatic updates (3.8.1 to 3.8.2 or 3.8.3) even if you don’t check the box for automatic updates. I don’t, and never will, want automatic updates on my wordpress: too many plugins and themes have a lag to the wordpress core deployment schedule. (I now know I can just add a line to wp-config.php, but the Softaculous interface could be clearer about the automatic update deal).

Am now in contact with the hosting service to look at solutions such as emptying webcache, restoring from their own weekly backups, their own diagnosis of the faulty redirect route, etc.

I’m looking for a solution that will do one of the following:
help me know what causes the redirect error so I can target the problem-solving
help me regain access to wp-admin login and the dashboard