What about the following idea: Always take the top-story off the front page and instead only show it on the "new" page? So the front page remains very useful, but if you want to look for the very top story, you also have to take a look at the new ones. Couldn't this be an adjustment to better "pivotize" the signal/noise problem?
(Addition: It may be better to take the two (or three) most popular stories.)
