wittenbp,
" I would like my blog to be visible to everyone, including search engines (like Google, Sphere, Technorati) and archivers and in public listings around this site."
From what you describe, the List All plugin and the Privacy plugin are both behaving as expected.
When a radio button is clicked and saved on the Privacy Options page, the "public" in the database is changed to some number, 1, 0, -1, -2, -3. De-activating the plugin will not change that value, or restore it. The value must be saved again to change its value from -1 to 1 to be "listable" again. "1" is the only value to get the blog listed publicly ... any arbitrary value other than 1 removes it from a list.
If you want the List All plugin to show a different list to logged in users, or subscribed members, or the SiteAdmin you'll need to add/modify conditions to the $wpdb query in the List All plugin.
The following example will list a 100 blogs for a SiteAdmin with no regard for the "AND public='1'":
if( is_site_admin() ) {
$blog_list = $wpdb->get_results( "SELECT blog_id, domain, path FROM $wpdb->blogs WHERE site_id = '$wpdb->siteid' AND archived = '0' AND spam = '0' AND deleted = '0' AND last_updated != '0000-00-00 00:00:00' ORDER BY last_updated DESC limit 0,100", ARRAY_A ); }