The Administration widget and the menu at the top of the control panel mostly comes from menu.ascx.cs in the admin folder. It looks at Web.sitemap in the root folder to see which items/nodes in the sitemap are accessible to you.
You could try removing the "rights" attributes in the Web.sitemap to see if that makes a different. You'll see in Web.sitemap those attributes that look for example look like:
rights="AccessAdminPages". You could try removing that part completely to see if it makes a difference.
If that doesn't make a different, in menu.ascx.cs, you could try updating the line below (line 99):
adminNode => adminNode.IsAccessibleToUser(HttpContext.Current)).Where(
... changing that line above to:
adminNode => true).Where(
I'm not sure if that will help, and if so, why it is not working currently.
This menu.ascx.cs file is for the .ASPX pages. I think the CSHTML pages (dashboard, themes, extensions) has its own version of this control.