Watching the second video, I think he could get the weight off the nose wheel sooner, with full back elevator, and then as the nose wheel clears the ground and the airspeed comes up, he can keep the nose wheel just above the terrain. Those huge elevators on a 182 will allow getting the nose up within the first 50-75 feet most of the time, unless there's a couple of huge guys in the front seats and nothing at all in the back, which can bring the CG right to the front of the envelope. The nose wheel adds a lot of drag in soft stuff, so getting it up ASAP is good.
The other mistake many people make with a trike is pulling the nose up too high for soft field take offs, which then adds a lot of aerodynamic drag and actually slows getting into the air. That's why you see a lot of trike trainers with dinged tail tie downs. I've never dragged a tail tie down yet in all these years, but I decided last year to add a skid to mine, just in case I was ever a klutz, because especially when I've been camping, I have a rearward CG. Not lifting the nose too high is especially important in high DA situations, because you need to minimize aerodynamic drag moreso than at lower altitudes, where you have more lift and power.
One of the issues that we've talked about is that our training is often unrealistic. Too many FBOs prohibit using their airplanes on anything but long and hard surfaced strips, so that often enough, students never get any real training in either short or soft strips--and as we know, often enough, those are combined in the real world. The Deakin method of holding the nose on the ground until Vx for a short field take off just isn't logical, when the strip is also soft. Using the first 1000' of a 10,000' x 150' hard surface runway as your short field gives you no idea what it's like to come off a short narrow, possibly soft, strip with trees at both ends and on both sides.
One of my buds is a low time private pilot who had to stop flying when an expensive divorce took all of his funding, but he's flown with me quite a bit, including to OSH once. He learned to fly with Aims Community College in Greeley. One Fall day a few years ago, we went up just to take leaf pictures. After we'd taken off, I asked him if he'd like to fly on over to Marble--I had told him about it, but in all of his training, he'd never been into the mountains. So we did that, and some of his reactions were emblematic of his unrealistic training.
As we dropped down into the canyon, his first reaction was that we were awfully close to the canyon walls. I was on the right side of the canyon but not hugging the wall, but several times he said, "aren't we awfully close to the wall?" Then when we turned up into the Crystal River canyon where the Marble strip is visible, I said, "there it is", and he said, "you've got to be kidding--down there?" Marble is not a difficult mountain strip, 3800' long nominally and plenty wide, but to someone who'd only flown out of GXY and FNL and a few other hard surfaced and long airports, I guess it looked pretty tiny. It was quite an eye-opener to him. Incidentally, our take off that day is the one in my Youtube video:
https://www.youtube.com/watch?v=LPNaGwZ2fA8Cary