I resolved a coockie issue with access to local copy of your site.
I can not repeat the problem with admin menu access. Testing showed that admin menu access works as expected, look this video.
Local copy differences: “iThemes Security” plugin is not active. I can not activate it for a while as I did not use SSL at local development environment yet. I hope to resolve this configuration issue and proceed if you give me more time.
It would be good if you send me (via email) a fresh temporal login link for superadmin user. I wish to compare some settings with your live site.