Here’s a few interesting breath-holding tips from Gorgo over on the Seabreeze forum:

Learn to hold your breath and just chill out underwater.
The feeling that you are going to die if you don’t get a breath is just that, a feeling. It’s a reflex caused by CO2 in your blood. It has nothing to do with the need for air. One thing is almost guaranteed, if you breathe under water you will most likely die.
Once you can control the urge to breathe you can go deep to avoid nasty stuff and survive hold downs and assorted tumblings and come up comfortably when all the action has ended.
I have always surfaced with one arm over my head and one arm extended upwards. You should be able to do that with a paddle in the extended arm. In normal surfing the danger is that boards get popped upwards then come down on top of you. With SUP you still have that risk plus the mass of this aircraft carrier being washed into you.
I think with a SUP it is a good thing to just go with the waves and run away rather than trying to beat your way through white water. With the faster paddling speed of the SUP you can usually get all the way out in a lull rather than fighting set waves. Or ride reef breaks where you can paddle away from the impact zone.

Seabreeze Forums! – Stand Up Paddle tips for a newbie in the surf