There's no way to independently control what is shown in the Latest News includelet, and so yes, as you say, if you set up a schedule to "unpublish" an item then it will remove it completely from the site.

One option would be to use the Item List includelet to choose explicitly which items you want highlighted on the front page, though this would require you to manually edit this every time you had a new news story you wanted to show.

I can't think of any way in the system to have an individually configurable schedule to remove items from an includelet that doesn't also unpublish the file.

Thanks

Joe - Voice Admin