I called RC and they do not offer rooms with balconies on 3 or 4 day cruises.
The Majesty Of The Seas has a whole deck of balcony cabins (deck 10). It's just that they are all classified as suites. There are no standard balcony cabins on the Majesty.
The length of the cruise doesn't matter. I just did a phantom booking and got to pick from any category from Junior Suite and larger. The Royal Suite is even open on July 4.