"Even a big wave, though, is going to pass by and allow you to surface in a relatively calm lull. A tsunami wave is going to continue to pound you into the shoreline as it drags you into land, because no lull follows the initial wave."
The only moving water in the initial wave, or in any wave, is that which is at the breaking edge. Once you surface after the breaking edge has passed, the wave will likely move you many yards towards the beach but it will not be as rushing currents. Instead the whole ocean will move toward the beach. It will seem very calm.
The real danger will come when currents start moving back out to sea. Then one wants to swim with the current and probably grab onto anything large that floats by.
I have surfed big waves. I know about this sort of thing.
I would be very interested in your opinion then of this particular video
I'm afraid I just can't agree. After the leading edge water will continue to move at 30MPH when you encounter a tsunami. I don't know of anyone who can swim against or navigate in a 30MPH current, and I know world class swimmers.