I actually did this a while back with the first 26 combinations for SKK. Not necessarily 'fixing' since I wouldn't call them broken. But focusing on getting to the heart of each one and what the purpose is/what it's trying to teach and streamlining it.
To go with combination one and your video - First thing is what is the combination trying to teach? To me, it is trying to teach an option for entering into range to take someone down.
With that in mind, the step back and cat stance is not needed. You also don't need to have your hands down by your chamber (not sure if that's a different in training; we learned all of them from pine tree stance with hands up, not in chamber).
So instead, take that out. As the person comes in, step diagonal to the right to avoid, and at the same time start with the wrap. Wrap won't be perfect, but particularly if they go to a guard, you can wrap around the guard. The other hand stays up in guard as you go in, with the two strikes and takedown. It makes it quicker, more effective, and still teaches the general principle. The only issue is that it's tougher to handle the first punch (and IMO my variation works better against a hook or looping strike. But my other issue is almost all the combinations are based on frontal jabs/step-in punches).