I've been wanting to pass on some ways I use to roll waves. They're alternatives to duck diving, which I've never really figured out on a mat. I'm sure lots of your readers might know them, but mat gremmies might appreciate the info. Getting out the back is extra challenging on a mat, so I hope these tips help (I made the usual dorky drawings).
The first is for rolling bigger whitewash (smaller ones you can duck dive or if you're slick and savvy, ride up like a ramp). I think of it as the mat version of turning turtle, and it works surprisingly well in quite big surf.
As the white water approaches, get off the mat. Turn your back to the wave, grasp the two back corners of the mat. Just before it's about to hit, let your body shoot straight down underwater, as far as you can go (you can do a little kick/arm pull to rise up briefly to try to penetrate deeper). Body as deep as you can go, facing the shore, arms extended to the surface, only the mat above water.The wave will bend the mat flat (turtle) on the water's surface, and your straight body acts as an underwater anchor. You lose surprisingly little "ground". Again, it works in pretty big (whitewater) waves.
This image might better illustrate the described posture:
The other technique is probably totally obvious, but what the heck. This works well for punching through a pitching wave, and I'll choose it over a duck dive every time. It's just rolling off the side of the mat, grabbing one front corner with one hand, and swimming through the lip, pulling the mat through, sharply, behind you.
I think you recounted GG describing it in your "Inflatable Dreams" article, about ripping the corner off a Hodgman at Sunset Beach. This method just works well in a lot of situations; possibly even better than punching through with a hard surfboard. Plus you can enjoy the view of the curling lip.
Best wishes and happy rollings,
PS: Next time, I'll attempt to diagram alternate tonguing while blowing up your mat :)