Then I don't think we do "irimi" as such. Just two days ago, my shihan was explaining to me how "everything is ayumi." For him, it is a more inclusive term than just meaning to step or walk.
Messy is good and real. Your vids are always interesting. Some differences I see in your applications are that my instructors would probably attack the face or neck with the hand that "enters" first. 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. 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"!
See what you think for yourself here
Enbu punches are usually straight jabs, but we also train against swinging/hooking punches, as you showed.