There's a metal cable that connects the climate control unit to whatever it is that directs the air flow. The cable could be seen underneath the dash directly, and pulls on a air redirection mechanism (blend door? or something like it) in the same way a brake cable does on a bike. For whatever reason, the mechanism didn't have its entire range of motion, so when the setting was on "blow through dash", it still blew through the floor vents. I could physically move the mechanism though to obtain the "blow through dash" setting.
I added a small kink in the cable to help the mechanism go all the way to the "blow through dash" setting. This probably means when I turn the dial all the way the other way, it will still be blowing on the floor a bit while also blowing at the windshield, but it seemed like a good trade.