If I were talking to someone who is fairly familiar with birth culture (in the US) and I said that I have had unassisted births, they would take that to mean that I did not have a medical attendant present in any capacity. In popular usage that's simply what it has comes to mean. If people generally thought it could mean a wide spectrum of things, it wouldn't really be useful for me to bother using the term, would it? But they don't, so I think it's most reasonable for people to use the term according to that definition. That's why I don't agree that anyone ought to define it anyway they want to. It's not practical, so I don't see the point.
So to answer your question, I wouldn't label that kind of birth (described in the OP) anything because a label doesn't yet exist for it. I'd just describe it. Cumbersome, but imo necessary for the sake of communication. The funny thing is that I do that anyway -- even though my births do fall under the generally accepted definition for "unassisted", I don't use that term myself because I don't care for it. I say instead, "I gave birth at home without a medical professional present and with only my husband in attendance." I might go on to say, "it was fully autonomous in the sense that no one managed or guided it, it was instinctive and primal." Then someone will say, "Oh, it was unassisted" and I'll say "yeah".
To describe a different scenario, I might say, "I had a physically unassisted birth with the midwife sitting in the corner observing." (And in fact, I did have a birth like that, and I generally refer to it as a "midwife-attended homebirth".) To just call it "unassisted" would be misleading, given popular usage of that term.
What wonderful insight you have!
: Exactly that.
