I wouldn't mess with the fipple; you can't really change much on one without messing up other notes.
One thing you may want to try is something called the "acute bend" that I've heard about on ocarina. When you start to move up into the high notes, bend your head down so that the ocarina is parallel to your sternum. That often clears up the airiness of the high notes on the thing.
There's a dude on YouTube called David Erick Ramos who is sort of the king of all things ocarina, and he's got a ton of helpful videos up. You may find them helpful.
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