I just posted the comments below on Board Talk re response to a 'tippy Speeed' however thought they would also be relavent here.
As a once whitewater kayaker where the only thing that keeps your head above water is your skill with the paddle I know that a SUP paddle is not just a blunt instrument for propulsion. Waving the paddle around in the air to regain balance is far less effective than having the paddle actively engaged with the water. To remain stationary you can do a figure of eight type of 'stir the pot' stroke to provide youself with very strong 'outrigger'.
Adding to that, a concept that has helped me is at the point of feeling you are loosing balance quickly drop by bending the knees as if sitting your bum down on a chair rather than allowing your torso to bend forwards with straight legs.
Watch the hot shots on tiny boards in tough conditions and you'll see the paddle is rarely not in or skimming the water.
Learning to use your paddle more will mean you can enjoy a smaller board. Best thing about a smaller board is less on the end of your leash in the white water or going over the falls!