Using Drupal's database for Apache authentication
I did in the past use the export_user_db module, but it is similarly lacking in D7 support.

I am now using modauthmysql quite successfully with D6; I also have an auxiliary module that I can publish to do single-sign-on between Drupal and Apache-authenticated sections of the website.

You are correct that the lack of a Drupal-7-compatible password hash is a limitation, but I don't think this would be too hard to add. Contact me on d.o if you would like to collaborate.

http://drupal.org/user/438598

If you really only need to serve static content, serving it from Drupal per the other answer is easier and better.