the plugin I mentioned is quite flexible and I am sure you can modify it so it does what you want.
basically, you can assign a default user by whom the "posts" are written, aka setup a user that is allowed to publish posts, tell the plugin to take that user as default user, then go ahead and modify the plugin form so users on your homepage cannot input their usersname, and the plugin uses the user credentials you created for the default user.
=> every post published by this plugins form on your homepage is treated as published by the user you created and because that user is allowed to publish, posts are automatically published.
keep in mind that I remember seeing this on the plugins to-do-list: feature to select to which category the post is published... you might contact the author though or change it yourself
good luck :-)