You have outlined one way to do this today. In general, you will need to create multiple copies of an alert (with different underlying searches for each different scope).
One tweak that might help is that alerts and other content can be tagged, and the my content widget that shows the alerts can be filtered by tag.
The other thing that may save you some time in creating the alerts is that you can select multiple alerts in the "content" section of the product and mass export them to XML. You could then edit the alerts and mass import them, which may save some time.