Thanks for the tips. I already had the windshield looked at by a repair shop, and they couldn't find the leak. They pulled down the front of the headliner to blow compressed air, but didn't find anything. I took a look myself, and saw that there appeared to be a small gap around one of the fastening clips, so I had them seal it. That was a couple months ago, and I thought it solved the problem. Evidently, it didnt. The leak did move to the center of the windshield as opposed to the driver's side though.
I would like to avoid replacing the entire windshield, but may have to. Apparently the windshield is in one piece (trim and all), and can't be repaired (sealed) from the outside.