I figured out what it was! I had "Split Application Binary" checked in the Player Settings --> Publishing Settings, which caused my Android app to publish an .apk file AND an .obb file. Global Variables are stored in the .obb file, so when I side-loaded the .apk file onto my phone, I forgot to include the .obb file so it never had any Global Variables to reference.
The solution was to UNCHECK "Split Application Binary" so the .obb file is never created. Now everything works (side-loaded or not).
Thank you for your help, I appreciate it =)