So . . . I carried a tripod this time! Alas, the wind was constant, so long exposures for still photography weren't all that practical. I ended up using it exclusively for video.
Speaking of the wind, notice the last shot in the video. Just afterwards I turned towards the waves to take a still photo when I heard a soft thud in back of me. Yes, the little Nikon I've been using for video had been knocked over by the wind, while still on the tripod, and was buried in the sand. The lens refused to retract for a while, but a little prodding at the grains of sand with a Swiss Army knife seemed to do the trick.