Redirect to home after NODE_ACCESS_DENY
The idea of creating a menu entry to redirect in the case of a 403 is fine, except that you need to configure the core handler to point to it, which is the element missing from your question (it's mentioned in the comment you linked to).

Once you have defined your menu entry go to Administer > Site Configuration > Error Reporting and set the value of the 403 page to the corresponding path.

Now the page callback for your menu entry will be invoked whenever there is access denied, so you can supply the appropriate logic for your needs.