From my background, I want structure and definitions. It all depends on whether it would be possible to determine the fundamental issues around which there could be broad agreement, and then to determine a vocabulary or method by which they could be defined/illustrated.
I believe that AT is built from fundamental elements, and a syllabus that has a page or two of introductory waffle, and then lots of tables illustrating a set of predetermined moves, has got it completely wrong. However, another approach could work better, but is unlikely to come out of one of the teaching societies, unless, existing members take up the social dance at a high level, and then write a text themselves, and get it adopted by their peers.
It must be possible to articulate the basic principles of this dance in a form of language that can be shared with others. How is the cross led? Is the lead different in cross system, and if so, how (and why)? What are the mechanics of an ocho? How is it danced and how was it led? The development of a 'technique' needn't be limiting or prescriptive if it is prepared in the right way and with the right approach. There are lots of ways of doing all sorts of things, but a basic syllabus could aim to illustrate a simple way to dance particular actions that would work for most people, most of the time. Beyond that, comes personal development, individuality and flair, but most of us have those attributes only to a modest extent...
Different people learn in different ways. I might be similar to you, in that I also like to have fundamental structures, along with definitions. I refer to that as the analytical (or geometric) aspects of the dance. That help me to learn and understand. However, I still have to practice to become proficient at executing anything. If I can't become proficient, usually it is because, I didn't understand it properly, or didn't get all the info/details I needed, or something like that.
For me, I actually have two categories of "fundamental" moves, that I title (mostly in my head) the "Micro" and the "Macro", fundamental moves.
At the micro level, there are three: the foot move, the weight change, and the pivot. Pretty much everything can done by combinations of these three things.
At the macro level, there is walking, rock steps, the cross, ochos (front and back), and the giro (mollinette). The "adas" (AKA named steps) I don't consider to be fundamental steps (although others are free to disagree).
The other "fundamentals" (but not really moves/step) that I currently define, are the embrace(s), and the rules for lead and follow.
This is (more or less) the model that I use internally to organize things. However, you still have to be able to execute, which requires practice, balance, and musicality, (in addition to understanding, whether it be at a conscious level, or at a subconscious level).
Using this model, I'll address one of your questions (about ochos). An ocho involves a foot move, pivot, and weight change, thus once you know how to lead those three things, and understand when they all occur in an ocho, you then are able to lead it.
BTW, the model is still a work in progress. I actually do think Musicality is a fundamental (at least on some level), but I haven't spent enough time thinking about the specifics of the analytical aspects (stuff that could directly be taught, like various rhythms/patterns) vs the more artistic/subjective aspects. And there probably are a few other aspects that I haven't figured out at all yet.
