Interesting. All 3 of those looked similar to one we do called Sorinji Sanchin. They were probably all derived from the same form way back in the day. They are all Chinese White Crane, what I do is Okinawan White Crane. There's not one technique we use to generate power, its a combination of a lot of little things, and timing them correctly.
The first guy (yong chun) doesn't look like he is generating any power, but I can see where that form was more for exercise. If he were to loosen up and do it more like the other 2 guys he would have power. What you saw as sucking in the stomach was actually him raising and lowering his hips. Raise your hips up to project power upwards, drop them to project power downwards. For instance, in the sparring session you described, lifting your hips up could have helped the uppercuts.
The other two guys were using their entire body to generate power. They were exaggerating it quite a bit, but the principal is the same even if you are more subtle. However, don't think that the big movements you saw where they dropped down and raised back up to strike was just pre-loading. They were both dropping their weight onto their opponent and pulling them in, which (if done right) will open up the next spot you want to strike (most likely the neck in this case) Just like the hips, raise your body up to project power up, drop your weight to project power down. Its a lot more powerful to drop your weight, but it seems all the good targets are up high. If your weight is already down low, you just need to find a good target up high to hit, and vice versa.
Another thing the last two guys were doing that looked a lot like us was the whip-like strikes. I don't want to get into a physics discussion (because even as smart as I am, I know I don't fully understand physics as it applies to martial arts), but think we can agree that in order to hit something hard, you need mass, and you need to be moving fast. The goal of the way they are whipping their strikes around is to get the speed. Its not as easy to do with close in punching, but its always effective with kicks. The guy doing trembling crane seemed to be using his hips wrong, which is probably why his strikes didn't have the power the shaking crane video did. Well, that and he looked much older, so I'll cut him some slack. But he kept throwing his hips back then he was striking up. This allowed him to keep his balance, but it took all the oomph out of the strikes.
One other thing that none of the 3 were doing right was foot positioning. Actually, he may have been doing it in shaking crane, its hard to say because of his messed up kung fu stance (I say that jokingly, it doesn't mean its bad, just that I'm unfamiliar with it) and the fact that I could not see his feet. If they were doing this correctly, the feet would have been constantly shifting back and forth between nihanchi and pasai (or whatever you call your basic stance).
I generate power by rotating my hips, torso, etc too. It can be added in to the rest of this stuff, but its hard to see it. That's how I get the whipping action, whereas the shaking and trembling crane guys were using big movements.
I'm a youtube newb, can someone explain to me why those last 2 videos kept automatically loading a new video when they finished? And more importantly, how do I stop it? It was very annoying. I looked around a little for videos last night and came up dry. My google-fu is very weak.
-h (I think this where I'm supposed to point out that I speak for nobody but myself. And that my opinions do not represent those of my teacher, my employer, my friends, or frankly, any sane person.)