Success!!!
@ProtoTerminator Your advice steered me in the right direction, but since my solution had to be a little different, I’m going to detail it here for the sake of others.
As I’ve discovered over the course of this thread, Addressables keeps some platform-specific files in the Library folder of your project outside of the Assets folder. When building locally, it copies these files into the StreamingAssets folder and then deletes them after the build. This way, your program can build for multiple platforms without you worrying about conflicting files. However, since Unity Cloud Build does not have access to your Library folder, it cannot copy these files for you.
What I essentially did is manually copy the folder Library/com.unity.addressables/StreamingAssetsCopy/aa into my Assets/StreamingAssets folder and push my changes up to the cloud using Unity Collaborate. This gave me a build that worked.
It’s important to note that building locally will delete that folder out of StreamingAssets again, so I will have to repeat this process every time I build from the cloud. I’ll probably end up writing an editor module that does this whole copy process and then starts the cloud build from within the editor, but one step at a time.
Thanks for your help, @ProtoTerminator . If anyone needs me to explain this better or differently, let me know.