Sorry it took me a while to respond (family and work take priority and stuff) but I did want to thank you for the info and the analysis. I get what you're talking about and I think it's something pretty deeply embedded into the practice of jujutsu/aiki systems - that notion of connecting things with the right feeling is table stakes to make any of the techniques work. The trick is always in the transmission, I suspect, whatever level the teacher shows will either be grasped or stolen by the student (or lost in subsequent generations) and so on and so on. I definitely think it helped inform your work with swords and vice versa.
Where I'm trying to get at, though, is in the corporate knowledge of "how internal strength works" is that connecting and moving the insides is but a piece. If I use Tohei's model for discussion purposes, the notion of "relax completely" as you know isn't fall down, but let frame, bones, ligaments and muscles work together appropriately without unnecessary tension. "Keeping one point" is akin to mind direction of ground/gravity forces to the point in space they're needed. "Weight underside" is another term for the physical expression of ground/gravity strengths.
So to your point, tenouchi seems to somewhat assume some of those other things are taken care of and more towards a means of application (or better aiding the application, I should say). Which sort of circles back to one of the vulnerabilities in the approach is if the goods aren't both developed to a high level and shown explicitly in a form that enables the transmission AND I think one of the reasons for the multiple modern interpretations of ki/qi (just look at the "To ki or not to ki" thread over in General).
Your example on polishing is a good one. I'm going to make up something, say that originally, the reason for the awkward, cramped position was because the only materials available at the time required it. Say, that additionally, the kind of force required to actually move the materials together to effectively polish, was a different kind of strength than just shoving by rote over and over. I can totally get how a kind of internal strength was developed doing this. Same thing with farming instruments creating a kind of bodyskill. Or the notion of the laborers carrying heavy baskets on their heads, or Bhutanese porters carrying unusually heavy loads up a mountain. Not superpowers, but body technologies built as skills and conditioned as strengths.
But these are the very basic, entry level types of bodyskills in the corpus of IS. Actually, I don't like the way that reads, because it sounds dismissive.
What I mean is more like, you have a spring, a swivel and a flail. Each on their own can be very useful, but when combined can generate seemingly unbelievable power. Yet, each piece requires conditioning and tempering, then must be correctly assembled and fit together.
That's kind of how I look at internal strength. There's a reason the qi/ki of heaven, the qi/ki of earth and the qi/ki of man are described individually in the classics yet they all fall under the rubric of an individual's ki. Just like Jin is the expression of ki, there are many sub versions of jin while only being one jin (cue highlander). Which can be expressed as the ability to feel your ability to manipulate ground/gravity, the strength and/or subtlety (strength AND skill) at which I can manipulate my gravity/ground to combine with your gravity/ground, or seemingly remove your connection to gravity/ground -- all could have different definitions of a jin application while being in the categorization of Jin skills and strength.
But there's more!! The jin skills and strength, combined with the strength of the body connections you conditioned and skill you've trained in applying them (how well you can "relax" into the softer power of the bones, muscles, ligaments working together) become part of qi/ki skills/strength which then would have ramifications in how they're trained and expressed within a martial art. What's frustrating reading the descriptions such as these articles referenced is that in the case of Takahashi's, he's only hinting at some things or saying something else about as helpful as "use ki" here (to be fair, most of the verbiage in a lot of "teachings" is about as sparse) but marrying it inevitably in such a way to a specific application or limited movement (ie. wrist grab, put power at the tops of wrists BUT use your skillful and highly conditioned ki in a way that your entire relaxed, but strongly connected body moves as a whole
Gets daunting and I somewhat blame as the (maybe intentional) reason it's not being taught as openly (either it isn't well known, still, nor well understood - or everyone's "already doing that" and it just isn't that big a deal and you automatically "get it" when you do techniques). So, from my casual observation it seems like the Jin/Connections skills are most obviously referenced and required to make any of this stuff work - while still being not very explicitly shown or taught. I find it interesting that the Breath/Harmonic stuff gets doesn't get as much play other than in the ritual or body coordination sense, though there are some that do drop the nuggets that get there's more going on there, too.
And I think as these things get more well known we'll be able to keep having some more informed discussions based on what's observed, hinted at, etc. At this point, it's just a fun facet of my hobby - even if it's made it much more difficult to participate in somebody else's idea of a martial art