I watched the steep portion of the video first, followed by the upper/less steep section where you appeared more comfortable making carved turns. I've so far in my 50+ year ski career taken one lesson (if I had any as a kid, I can't remember).
Preface: I'm not a ski instructor, and don't make any claims as to be able to describe how to ski. Although I can tell some things from watching the video, it's not a complete picture. Q's: What skis are those? how long, how flexy? They look to have quite a lot of tip rise, not good for carving on groomers, worse in bumps when the outside edges aren't high in the air. Be careful calling those moguls icy, as while they might be "western icy" and toothy, sucky that ain't.
Marcus is wrong, there are moguls that suck, especially the two or three in a row that caused me to be too far in the back seat, more than my poor old ACL could take. (Goshawk at Beaver Creek, old toothy moguls capped with 4" of slushy new snow). Or maybe he's right, it was "something else...."
The one Alpine lesson I've had in the past 50 years was because I somehow got an early-day 1-hour private lesson for free at Snowmass, sometime in the late 90's, shortly after I got my first pair of shaped skis (Salomon X-Scream). While I felt that I might be able to pick up a couple of pointers, I was shocked at how much I was able to learn with a lesson on moderate groomers!
The most important item I learned was "let the ski do the work" It was pointed out that my turns were more Z-shaped than S-shaped, simply looking down the fall line and reaching out to plant the inside pole to initiate the turn, rotating and weighting the outside ski... that's all. Only slightly more complex in moguls, pick your line, plant your pole, on to the next turn!
Watch your hands and your hand shadows.
What stood out from the video is that it appears you aren't reaching out to plant your pole, and this results in over-rotation on some turns, putting you off-balance. Your arm-shadows ought to be zooming out away from your body shadow a whole lot more. It's really surprising how many very good skiers try to make it down the hill using just their skis, poles hanging there primarily for ornamentation, and making in Z-shaped, not S-shaped turns
Secondly, while turning on the spine can be a needed strategy sometimes, using the spine consistently to avoid carving in a perfectly good trough just below might be an indication you aren't comfortable carving into the the trough in steeper, toothier bumps, as well as you'd achieved on the upper, less-steep section. Chopping the spine and turning with just the ski edge under the boot, while effective, could be interpreted as a coping strategy for not feeling able to adequately control your speed through carving.
A couple recommendations: (without knowing anything beyond the videos)
1). Try, on a less-steep, smaller-mogul section, actively reaching out with your pole to start your turn, and resist rapidly turning your skis, let them ride the ski-edge around, regardless of where on the next small mogul the turn takes you.
2. Experiment with different turn/pivot locations in small moguls with moderate pitch, try skiing wide S-turns as well as zipper line quick-as-possible turns. This will help to identify your comfort-limits, and provide some clues as to skills that need developed or practiced. Of course, baring your skiing soul to the critiques of the internet universe is pretty good strategy too, as long as your ego isn't as hard-edged as those moguls.
3. (advice I need to take for myself) Find a group moguls/steeps clinic, you might be surprised at what you learn....
4. When you have an opportunity for soft, powdery bumps, just let it rip for fun, without much (real-time) analysis. Or maybe while skiing with friends, ask them to watch for something specific, like "watch my pole plant, here's what I'm trying to do".
Are you an engineer
?
Of course SSSDave must be, there's no other logical explanation!