Here's an application I've been exploring for the first three moves of Pinan sandan. Basically, a punch comes in and you block to the outside. The second punch comes in; you trap the first hand down and you block to the outside of the second arm. You now have his hands crossed in front of him and a twist or shove of his arms throws him.
In aikido, the throw is jujinage, here is some footage of the idea: https://www.youtube.com/watch?v=CTqCGnTEq4Y
The same concept is a basic technique in mantis kung fu, some footage starts around the 1:10 mark: https://www.youtube.com/watch?v=5XE4gSddlYI This version is less "elegant" but looks more practical. I really like the old guy in this one.
Note that your hands have to "stick" on the blocks. Not grab necessarily, but at least remain in contact.
Hey Heath. Your video is set to "private" so we can't view it.
Hey Andy, thanks for the tip. It's not my video and the owner must have made it private recently.
Here's another version that is pretty close https://www.youtube.com/watch?v=X8cnmXGaOWg&t=202s except you have to make the first block inside-to-outside instead of outside-to-inside.
I can't see videos because I'm at work, but I can imagine the application you have in mind, and see how it would fit those movements. What I have found, though, is that you will be very hard-pressed to actually get the lock you're referring to from that entry, because (like most entries I've seen into this lock) it relies on your opponent not really trying to keep using their arms after they punch. Your opponent is going to try to pull their first punch back when they throw the second. You can certainly stick to it and follow it back, but then it's all the way on the other side of their body, and unless you grab it and pull it back across, chances are they are going to fuss with your hand before trying to punch you with it, again, because they don't want you to grab it. Meanwhile, you're trying to hold their second punch out so it can be locked, and if you're going to do that, you might as well just lever it across your chest and lock it that way. Admittedly, since I can't see the videos you referenced, at the moment, perhaps what you're proposing is different than what I'm imagining.
FWIW, my preferred approach to this lock is to get it as extra credit when doing a chest-lever armbar, and the opponent throws a punch or tries to grab my bracing arm, because they are initiating the movement of the limb I need to wrap around the one I already have extended and ready for locking. This is actually a henka application for the "elbow-wing"/backfist sequence toward the end of Pinan Sandan.
Here's another example of the same basic technique.
To be honest I am not sure whether you (I) could pull this off for real ... so consider these links "retweets not endorsements". I do think the move has the merits of fitting the moves of the kata fairly closely, and also it fits with Iain's idea that this form is mostly throws.
I have pulled this lock off in kakedameshi and bully sparring, against resistance, but it's not very easy to get to, and most entries to it I have seen just don't work. I may have to put a video together on it, because I do actually like it, despite the difficulty in getting to it.