Some differences I see in your applications are that my instructors would probably attack the face or neck with the hand that "enters" first.
As would I - the entering hand is actually an attack, but I erred on the side of caution and pulled it out because I didn't feel my control was that good on the day - I've been a bit out of practice due to extended illness. I went for a "soft" option, prompting some on other threads not to "flame" me for not using a more effective counter - I was principally illustrating the deflection leading into the enter.
The second hand is usually interpreted as the "safety" in case the first hand fails. "Ayumi" would come into play in regards to takedown--I would probably be told to "keep walking" rather than rely on upper body strength for the first one you show.
That's what I meant by messy. I wanted to keep walking, but Jed felt like a brick wall that day so I had to put some more oomph into it. Normally the "C" back and the "walk" through works a treat - almost no force required at all.
My sensei is also very picky about us using "ayumi" footwork when we do the second takedown you show. But the reality in sparring is probably quite close to what you've posted. I'm also just talking "different" not "better"!
Indeed - the footwork here is of Chinese origin and is also very specific. I lost my own posture a little at the end (also messy) but again, Jed wasn't primed at all and is non-compliant. And I'm always up for a challenge! I don't want to post something on the net where it's obvious I've chosen an easy target. I take the same approach to demonstrating to the class - if it fails, I learn.
See what you think for yourself here
Enbu punches are usually straight jabs, but we also train against swinging/hooking punches, as you showed.
Fascinating videos - absolutely loved them, particularly the first one. Very direct and simple entry, very practical approach and quite refreshingly different. This is the first Motobu-ryu I've seen, so thank you.