If you want to continue using basic authentication, then you can look into changing the authentication realm dynamically when you want a user to log out. The new realm will trigger the client to ask for new credentials to authenticate in the new realm.

I don't know if your current method will allow that, but you could do it with a custom mod_perl Authentication Handler.

Basic authentication is generally not considered that flexible when it comes to allowing users to log out, but the realm trick can work.

Cees