So, I have spent time since that last thread you reference, looking at the TKD version of this technique... (or at least what I see on youtube) and I found a few things that I thought were useful. (tried a few of them out on unsuspecting jujitsu students...) Rather than list what I found, I want to go through how I found them.
I started with the Karate version first, as I study that version. Also, the Karate version is in the lineage of the technique in question, at least partially. In the karate version, when the main hand chambers up to the side of the face, the back hand makes a palm up spear hand forward, instead of going back like the TKD version. This is taught as guarding the center line, while chambering... followed by the knifehand block. This can be seen as a spear hand strike to the solar plexus, followed by a block to the side of the neck. In karate, the open hand also signifies a grab. Instead of the back hand delivering an initial spear hand strike, it could be grabbing the gi, then pulling the guy into the block to his neck, or slowing down a little, pulling the guy guy in deeper and executing dump over your forward knee type throw. So, things to take here to the TKD version: the open hands can be spears, knife hands or grabs... the application can be during the initial chamber... changing the distance will change the outcome.
In the TKD version as I see it on youtube... both hands move back together, front one to your face, rear hand goes behind you, then both come forward to the position in the picture. Assume you are facing the other guy, he is grabbing your neck with both hands (dumb choke). When you drop into back stance, do it so that your "front" foot turns out, and your rear foot stays pointing at the other guy. The main hand comes up to your face, from underneath both of the guys arms, while your rear hand chambers behind you. Use the main open hand to grab the guys wrist. (if my main hand is my left, it comes under the other guys left hand, and grabs his left wrist) At this point, my main hand "blocks" which will extend his arm and his side, also rotating him to his right. If you are close enough, the rear hand knifes through his elbow... elbow break or arm bar. (I had to play with getting the distance right, but once you figure it out...) If you are closer, that rear hand can deliver a knife hand to the kidney or short ribs, which are now open.
There is a foot propping throw that we do, where you start facing the other guy, grabbing gi lapel and sleeve. I get the guy to suddenly take a step forward, while using my foot to stop his ankle, preventing that step. If he knows how to fall, it looks pretty cool, if not, he face plants pretty hard. In order to get that sudden step forward, my hand on his lapel, comes to my center, while my hand on his sleeve takes him forward to the far corner. It can look very similar to the chamber before the double knife hand. If you transfer your weight to the front foot, instead of the back foot, you could easily prop his foot for the throw. The hard part of this throw, is generating his forward step. You could take the propping foot out, so as to get closer to the TKD technique. Start in front stance, front hand grabs his lapel, back hand grabs his sleeve. Shift into back stance, using your body weight to generate the power, chambering your hands for the double knife hand block, further propels him past you. As the back hand comes forward, still grabbing his sleeve you can produce and nice arm whip type throw, if your timing is right... or just let them go.
Another art I have looked at a bit is Daito Ryu. They teach big motions first, then make them smaller and smaller. Since Funakoshi was further simplifying things for elementary students, he may have made things even bigger. Start with a cross wrist grab, right hand to right wrist. Its common to cover his fingers with your left hand, circle your right to the outside and produce a lock, in the downward direction. The Daito Ryu guy I train with, does this with out covering the fingers, if you blend right, its not needed. Then after you get the lock going down, he cuts horizontally back into you. This will put you up on your toes like a ballerina trying to get away from the lock. If you start the double knife hand thing from TKD, where the other guy has this cross wrist grab... when your back hand goes into chamber, it just needs to go to the outside of the other guys hand. As you roll your hand to palm up, execute the back side block to your chest, it produces the lock, and cutting motion through the other guy. You will have to make the motion a bit smaller and blend, but it works well.
I hope this makes sense... sometimes my writing leaves some to be desired when describing this stuff. But, by looking at where the technique came from, and by focusing on some of those things as I did the newer TKD version, I found some interesting things there that work for me. Whether you agree or get anything from this doesn't change the fact that when I looked at a TKD technique, looked at how it was done, where it came from and started playing with those ideas, I was able to learn quite a bit about things that had nothing to do with blocking punches. It helped my jujitsu get a little better. It helped my karate get a little better. It helped me figure out that silly Daito Ryu lock. I also got to throw an unsuspecting student quite far.... his face was priceless. Anyway, thanks for inspiring me to learn a few more things by looking at TKD forms and technique.