I’m not sure what could be going on with the app deployed on *.meteor.com, so there might be another issue, but for your app deployed on AWS using Meteor Up, you should specify the ROOT_URL including the right port.
Meteor Up builds the app for you. You specify the port in the config file. But meteor up doesn’t build with the URL specified, you simply type, “mup deploy”
As mentioned above, the ROOT_URL is passed on to the generated index.html and tells the client where to connect to. If your public URL uses a non-standard port, the ROOT_URL should include the port.