And now, from Blane Chambers, how he and his friends do it:
Best technique I have seen and now use is this one that Stewart Ferriman has wired.. One day I saw him in solid waves getting shacked without any problems from the paddle catching. Right then and there I knew it was the most productive way to ride the barrel without the paddle getting caught… Later I got these shots of him doing it… IMO The best way possible when the barrel isn’t big and I have pulled into many barrels and gotten smashed trying to keep control of the paddle. This way I can relax and enjoy the view… 
You basically ride the barrel just like you do with any other board complete with arm stalls if you like. I got my best barrels using this way and next winter plan on getting a whole lot more!