Its interesting to compare broaching in a boat and shuttlecocking in a hovercraft. They are related but different phenomena, related because in both cases they happen because the yaw (turning) forces on the hull exceed the maximum rudder force. That is, something is trying to turn the craft and the rudder is not strong enough to prevent it, so the craft yaws (turns) uncontrollably.
The difference is that the boat experiences mainly hydrodynamic (water) forces whilst the hovercraft experiences mainly aerodynamic forces. I say 'mainly' but recognise that both classes of vessel experience both forces.
To understand boat broaching you need to appreciate that waves are a bit wierd, in that the water moves both forward and back ward. At the crest, the water moves forward in the direction that the waves 'seem' to be going in, whilst in the trough the water actually goes backwards! If a boat sits with the stern on the crest and the bow in the trough, and it is not perfectly at 90 degree to the wave, the bow is pushed backwards whilst the stern is pushed forwards, turning the boat until it aligns with the wave. The end result is that the boat is left sitting parrelel to the wave right in the trough, and the next wave can roll it over. Very dangerous.
In the hovercraft, things are a bit different because it's the wind not the water that causes the issue. Often, the wind and waves are aligned (but not always). Hovercraft tend to have more structure (duct rudders etc) at the stern and in a side wind this results in more side force at the back than front. This makes the craft turn towards the wind, and if the rudders cannot create enough counter turning force, the process continues until the craft points directly into the wind.
So we see two main differences with hovercraft, which respond to wind forces and turn through 180 deg, and boats which respond to water forces and turn through 90 deg. The hovercraft is much safer, because it leaves you pointing into the weather and able regain control, whilst the boat leaves you sitting in the trough waiting for the next wave to turn you over.
I did say that both classes of craft do experience both forces , and the hovercraft pilot should be aware of this. When you surf down a wave, if your bows bury themselves in the next wave, they will experience a strong back ward force, and if you are not perfectly straight on to the wave, this will turn you almost instantly. I have experienced this, it is unbelievable how fast the craft spins in its axis and in my case rolled over, literally catapulting me into the water. This is a very dangerous combination of forces. Fortunately, it is easily avoided.
In a hovercraft it is imperative that you maintain enough lift to keep the craft out of the water. If you can see that it is inevitable that the craft will bury it's nose in a very steep breaking wave, it is vital that you hit it straight on.
Practically, the best advice is to maintain enough thrust so that you have decent air over the rudders to keep control, so use the brake (if equipped with one) or throw out a trailing rope with a few knots tied to the stern. Then turn out of the wind so that you are not running directly downwind, tacking if necessary to maintain your course. If you are still struggling to maintain control, shift some ballast (ie yourself!) to help turn the craft out of the wind. But above all, maintain your lift!
Ian