This actually is possible. Basically, you need to add a secondary domain (not an alias) and then execute this Google Directory API request:
You can run this command quite easily, at the time of this writing, by visiting https://developers.google.com/admin-sdk/directory/v1/reference/customers/update, scrolling down to the "Try It" section, and setting
customerDomain, and adding the field
customerDomain to the request body, with the value of your secondary domain that you'd like to make your primary domain (no www). Isn't that nice?
More detailed instructions are at http://www.saysjen.com/swapping-your-google-apps-primary-domain-to-your-secondary-domain-for-dummies/.