In my mind, mogul skiing comes down to the turn, which is the same turn to be practiced on a groomed run. I've pursued a particular style of mogul skiing that is direct and takes a particular type of turn. It's an easy turn to do on the groomed, but hardly anyone does it. It's worth spending a year, several hours each day doing these turns down the groomed. After you have it perfectly drilled, it's a neat feeling when you realize that you've automatically done this turn in the bumps, just combined with A&E. Normally, I wouldn't bother trying to explain this turn, because many others want you to do a different type of turn. Then we'd argue when people tell me my turn is a terrible turn to do. But, since you asked me specifically, I will give you my opinion.
Narrow stance, weight shift, tip the ski with knee angulation, shoulders square facing down the hill, hands in front flicking the pole plant out to the front, continuous cuff pressure throughout the entire turn (by pulling the feet back with the glutes and hamstrings, don't want to be reprimanded by Noodler again)
If you skip a few seemingly tiny details, the entire thing falls apart. The point is to get the ski to pop in a quick turn all on it's own. If the technique isn't right, the ski won't pop, and the turn will be too slow for the bump line.
If you let the shoulders lean, then you've decreased your hip angulation which decreases the edge angles. Since we're very upright with very low edge angles to begin with, that tiny bit of difference causes the ski grip to decrease, so the ski smears instead of pops, and it won't come around in time. So, you really do need to pinch the grape between the rib cage and the hips to keep the shoulders level. It does make a difference.
Forward pressure is huge, because it gives speed control with the tip biting in, and also the skis pop faster, so keep those hands out front (while still comfortable), not to the side. Every bit of COM forward helps as long as you're in a productive athletic stance that's comfortable and relaxed.
Upper and lower body separation is absolutely necessary to tip the ski with enough edge angle and forward pressure, otherwise ski won't pop.
Even for people that can start a turn with forward pressure, it's very common for them to release that pressure at the end of the turn, but then you lose your speed control. Keep the pressure on the cuff all the way until you step to the new ski. Let the ski do the work. If you have trouble dialing in this groomed run turn then do Javelin turns with continuous forward pressure and the hands pointing down the hill diagonally across the skis.
The end result is that the upper body is 100% stable while the lower body just steps from cuff to cuff with knee angulation. Looks like this. No worries if it's not your cup of tea, each to their own style.
Here's the Javelin Turn drill demonstrated by Patrick Deneen. Notice the constant shin pressure until the step to the new ski. You can do it with more exaggerated upper body separation.
