Scanning a website as an authenticated user is a common reason for people turning to Scrutiny.
The process necessarily involves some trial and error to get things set up properly, because different websites use different methods of authorisation and sometimes have unusual security features.
Scrutiny now has an important new feature. Some login forms use a 'security token'. I'm not going to go into details (I wouldn't want to deprive my competitors of the exasperations that I've just been through!)
There's a simple checkbox to switch this feature on (available since Scrutiny v6.4), and this may enable Scrutiny to crawl websites that have been uncooperative so far. (This may well apply to websites that have been built using Expression Engine).
All the information I have about setting Scrutiny up to scan your site (or member-only pages etc) which requires authentication is here.
Version 6.4 is in beta as I write this, if you're interested in trying it, please just ask.
Small print: Note that some care and precautions (and a good backup) are required because scanning a website as an authenticated user can affect your website. Yes, really! Use the credentials of a user with read access, not author, editor or administrator.