You've got a lot of balls and a lot of ski. I've got a few inches and 50 pounds on you, but I'm skiing 168cm skis. You could easily go as short as 160cm. Yes it's hard to believe. I've been moaning with every new pair that I've downsized all the way from 202 even as my weight went up and my height went down. Just do it.
Although this isn't the strongest mogul skiing we've seen lately, there are some good things to note. In the second clip, the first turn is a classic stem turn. Note the weight moving up the hill and the transfer of weight to the new outside ski. Picking up the tail of the inside ski and keeping the tip in contact with the back side of the bump is a great move. Another good thing I see is that you are not shopping for turns. When you finish one turn, you go right into the next one. In the second clip, all of that vertical motion above the waist is helping you turn. Another nice thing I can see is the use of the pole to stabilize you through the edge change. Finally, although a wide stance is generally not a good thing in the bumps, you are making effective use of the increased balance afforded by it. Except for one little bobble in the second clip, speed control is pretty good and you're in no danger of falling.
For those of you who are snickering, just remember "there but for the grace of ... shorter skis ... go I". Whether your handicap is long skis or pea soup fog, this is not a bad defensive way to navigate difficult terrain. Jack looks like the classic case of someone doing just fine on terrain that a lot of instructors would not take him on due to a large number of ingredients in the recipe for disaster. The difference here is soft snow and a can do attitude. Jack is making effective use of the skills that he has and is not getting in anyone's way. Glen Plake may be able to cruise control the bumps with long skis, but mere mortals are going to be real tempted to cheat just like this. And there's nothing WRONG with that. He's having fun and has not come close to killing himself or anyone else.
That said we don't want to fix things so much as give you new skills that will let you have the additional option of going on offense instead of being on defense all the time. Here are the things I suggest:
1) quick feet
2) slow feet
3) edge set/absorption
1) quick feet
(booming voice from the heavens) Get Thee Shorter Skis! Practice pivot slips where the objective is to turn your feet as fast as possible while the skis are flat on the snow. You should be able to this just fine. With shorter skis you should be able to do it better. Got that? Now do it even faster. Pivot turns will get your direction changed much faster than stem turns. This will give you more options.
2) slow feet
Some people are going to tell you that your stance is to wide for moguls. It is. But that's only a symptom. Look at the beginning of the second clip. Just as you start you are in a good stance width. But right before the first turn you stick your right foot down the hill to put the brakes on.
(Madden voice) Boom - you're in a wide stance. This is ok for a stem turn, but there is a way to put the breaks on via a parallel turn. Look at Dave (from the Davebumps2 clip).
He's got his skis angled uphill before he starts his turn. You don't always need this much to slow down, but you need to be able to put on the breaks with your skis in parallel. So where do the "slow feet" come in to play? Simple, instead of turning your feet right or left quickly, you need to learn to roll your feet onto higher edges RELATIVELY SLOWLY and let the skis put more shape into the turn. Using your edges more will give you the stability you need if your going to KEEP your feet closer together. Look how far you've turned and still have relatively flat skis:
In contrast, look at the difference in Jack's edge angles. He's on his new edges above the fall line.
As Sidecut has mentioned, doing good parallel turns and then transitioning those into short radius turns with edging is the best way to build these skills.
3) edge set/absorption
This is the big difference between offense and defense. Here you are sticking your right leg out and bracing against it.
This is forcing your upper body to fold over to absorb the pressure. What we want to see is both legs out a little less than the one leg and the legs bending a lot more. This will let your upper body stay more upright. Watch Johnny Mosely set his edges and then boom - absorb with knee flex. Ok - this might be an extreme example, but it should demonstrate the point.
Yes, you've got some new tactics to learn. Yes, those tactics are easier to learn on groomed terrain. But you can already do moguls. Don't let the naysayers stop you just because you're not doing it like the hot shots. You've got a road map for improvement. You can do it! But you do need to trash those war canoes.