Sockwater, I did a poor job explaining the problem. I'm not as slow as I look, I promise.

I'm working with someone else's code and trying to understand exactly what's going wrong.
I have a file called headlines.php. With the .htaccess posted above, you can access it via:
http://www.diabetesdaily.com/news/headlines.php OR
http://www.diabetesdaily.com/news/headlines/.
Or you could access:
http://www.diabetesdaily.com/news/headlines/page/1 OR
http://www.diabetesdaily.com/news/headlines.php/page/1
If I make this a 301 redirect it goes to 404. If I remove the .php from the .htaccess file, I get a server error. If I add a 301 redirect and remove the .php, it goes to 404.
Ideally, I think I want to make the last line a 301 redirect AND redirect from headlines.php to headlines.
Is this more clear? I feel like I can follow the current .htaccess, but I'm at a total loss how to describe what I want to happen.