Keeping only 1 "home"

if I have a site set private, with a "home" location for logged out users. Who can register and apply for accounts with a blog page associated with it, and then use this to direct it to a new "logged in" home, how can I set it up so that only one "home" menu is visible? If I don't publish the logged in one, it can redirect to it fine, but it doesn't respect the menu item choices. So for example I have it set not to show the page title, and have a page title different from the site-name. As soon as I unpublish it though it forces the sitename in as the page-name and attaches it to the front page.

So I'm either stuck with 2 home choices, or a borked logged in page because it's attaching information I don't want.