Deploy Meteor app and migrate the built-in, local MongoDB to a remote server where the app is hosted.
It took me days to actually get this working, so I figured I would write out the steps I took to finally resolve the issue for my own assistance in the future and, hopefully, to help others who encounter this problem.
.deploy folder in your app's directory
cd .deploy mup init
mup.js file to match your configuration. Here's an extremely basic example: