Looks like fun, thanks for sharing!
As a snowboarder;
Generally I like to try and keep my upper body quiet, I don't do a lot of stunts or anything though so I'm not trying to load up for any spins or twists etc - again generally speaking. Holding on to a stick and rotating the upper body in an opposite direction than you would normal for a proper turn, in order to lean on it, seems counter intuitive to me. Usually snowboarders who counter rotate the upper body are either A) beginners or B) park ride and do all the tricks and stunts (most of which can out-ride me about anywhere on the mountain anyway) and skateboarders, or C) performing some emergency maneuver i.e. like just about to come to a stop back at the lift when an edge catches (see A), or suddenly you are desperately avoiding the punk your on a collision coarse with who dropped blindly down across the cat track your on so he can pull some crazy stunt off the lip. I can see the paddle maybe helping make a tighter turn, but wanting to do so more than you are able springs from a lack of confidence or skill - or at least that's how I feel about myself in such situations anyway ; ).
Why I love hard pack - fresh groomers in particular, it is all about carving! No need for leaning on a stick when the carving is good and I'm laying in deep turns because I'm already leaned way over - technically the board is leaned way over, I'm more or less standing vertically on it - upper body quiet and balanced except for an occasional hand dragging the snow because it's right there so close. Not much different in fresh powder really, still in balance over the board, still a carve like feel, just softer and floating, more free in a sense.
Toe side turns for me are by far the most comfortable and easiest to perform. Heel side are more challenging for me, tend to make them shorter and quicker and tighter, harder to balance right, less comfortable, easier to loose the edge and blow out the turn, easier to break something if you stick a hand out to catch yourself ( a bad habit no no anyway) but I feel with the paddle, though it could catch you and support you and help keep you up, it would only make those heel side turns even more unbalanced, like a compromise, here throw your balance off with this but then catch yourself with it, if that makes sense.