I learnt to paddle aussie surf, racing skis and the shorter wave skis. These are by their very nature, tippy by any standard. feathered, offset, assymetrical bladed paddles were the norm and are used by ski racers and surfers alike. The reason for this is that they are a superior paddle in all conditions. One just has to get used to them.
To the original question, on the skis, I learned to use high and low, stern and mid-ship rudder braces as a matter of course and use these same bracing techniques in my kayaks now. These braces require the boat to be moving forward to have any effect at all. The blade is pushed against the water as it passes and can litteraly be a life saver.
Since moving into kayaks and canoes, i have learnt to do the sculling brace thingy a bit along with a few other pretty flash strokes thanks to Cadeppa (thanks mate
) but the good old high and low brace are priceless in the skinny boats I so love to paddle. I posted a small vid here somewhere of me negotiating very small surf in my beloved Southwind (Open, extended cockpit) and a single blade. I used what started out as a rear steering low brace which moved into a high, mid-ship brace for stability as the boat shot sideways down the face of the wave.