I've had good luck with Look/Rossi Axial/Turntable bindings. They seem to go on in deeper snow, with snow packed on the bottom of a boot easier than any other binding that I have used. If you do end up with a lot of snow in between you boot and binding, be sure to clean it up at the bottom of the hill though.
Tyrolia is the only binding company I trust. After problems with salomon, marker, and rossignol (look style heel), I don't think I'll ever be convinced to use anything else. My three pairs of tyrolias have been bullet proof in all conditions throughout the last years of my racing career and free skiing.
IMHO, I think that you're looking for trouble if you decide to go with a swivel heel skiing a lot of deep stuff..
Having skied most of my life on West Coast powder when skiing powder I know the joys of trying to get it off your boots after a fall. I have Salomon, Rossignol & Marker bindings. Of the three I found the Salomon heel seems to work the best when you don't get all the snow off your boot heel. The Rossignol heel pieces require less force to step into making them easier to get back into so I prefer Rossis for powder.