Hiding the main menu for strangers

Is there a way to hide the main menu for stranger level: none-no access to content or to get levels to work correctly?

1) I set the stranger settings in Membership | Options to none-no access the main menu still shows up. But otherwise acts how I want the site to behave. No access to any content for visitors.

2) If I create a new access level called visitors and then add in positive rules for 1 menu item (the register page) and 1 page (the register page). I get the one menu item I want and the page I want BUT, I can access ALL of the content of the site using search or just typing in the page. It is hiding the links to it but not protecting any of the content.

3) Negative rules are not a good option because I don't want to have to go in and set permissions everytime content is created.

4) I have also tried URL group filtering with little to no success.

The goal - #2 would be ideal so that I can just display one menu item and one page. But, as it is now, membership is not truly protecting content using positive rules.

Everything else seems to be working great. Keep up the great work!