Good discussion here, all! SCSA--good observations, too, about skiing the heavy stuff.
Here are some general (not necessarily applicable to any one person), practical tips you can try.
If you tend to ski in a tall, relaxed stance, lower it slightly to create a little more muscle tension throughout your body. This kind of snow wants to toss your skis around, so you want to "grip the wheel a little tighter" to exert a little more control over your skis.
Ski "two-footed." As Jonathan described above, if you pressure one ski a little more than the other, it will sink unpredictably, while the other "lighter" ski will float quickly up, throwing you off balance and often spinning you right around backwards. (I'll bet you saw that exact sequence more than a few times yesterday, if the snow was really deep and heavy!)
To help with this "two-footed" thing, adopt a fairly narrow (but not locked together)stance and MAINTAIN that stance--keeping the width of the feet constant and the depth of both skis in the snow similar. Many instructors recommend keeping "equal weight" on both skis, but I find that I don't succeed well with that thought. As long as both skis work together in the snow, the weight WILL be equal, so I focus on the stance and movements, rather than the pressure. Again, a lower, slightly more muscular stance than you might use on groomed "easy" conditions can help.
Finally, since skis don't go sideways well (or at all) in this kind of snow, you have two choices. You can leap the skis out of the snow, turn them in the air, then land and finish the turn with the skis bending and carving.
OR--you can make movements that don't require the skis to go sideways in the first place. This is where all the "carving" practice on the groomed snow will really pay off. Carving skis don't go sideways, so if you are really accurate, you can keep your skis down in the snow, slicing always forward, rolling from turn to turn, carving up the crud! This is an elegant, beautiful, and highly efficient way to ski crud. But it takes tremendous accuracy of movement. If you lose your balance a little on groomed snow, you can steer, step, or push your feet around to avoid falling. In heavy crud, you can't do these things, so a little imbalance is likely to cause a fall!
The first technique--"porpoising," launching out of the snow, pivoting the skis, and landing, is more energetic, but also more forgiving. Every time you leap your skis out of the snow, you have the option of placing them back down wherever they need to be for balance. Recovering is much easier. When the conditions get REALLY tough, especially when they are inconsistent--breakable crust, wind slab, etc.--even the very best skiers will revert to this turn-in-the-air technique.
Remember that if you tend to use a strong blocking pole plant to help turn your skis, it won't work reliably in deep snow! Use a smooth pole SWING, but beware of trying to jam the pole into the snow for either support or to create turning force. Use that fluid swing to help create rhythm and to keep everything in constant motion (it's easy to "freeze up" in these conditions)--but don't rely it for much else!
Above all else, remember this:
To get a good taste of difficult snow conditions...you've got to eat a little!