Thanks to a tip on Google+, it appears I found the solution. In the build.gradle file, the values for minSdkVersion and targetSdkVersion can be overridden. I'm assuming that this file is generated based on the manifest, and there's a bug in Android Studio that was putting incorrect values here. This is only an assumption.
The following images show what the build.gradle file was like before I altered it, what it looked like after I altered it, and what the Developer Console shows for this new apk after I uploaded it.