When you say three is the downbeat...
I actually didn't say that beat 3 is the downbeat of the measure, as is implied by the way you phrased that.
The word "downbeat" has a couple of different meanings, based on context. The dictionary definition is simply the first beat of the measure. When we talk about the downbeat in general terms, that's usually what we're referring to.
However, the term "downbeat" can also refer to the specific part of a single beat. In this context, we're talking about the initial moment the beat strikes, say, as opposed to the "upbeat", which for example might be the "and" count (or for that matter, any moment occurring within the duration of the beat that's not actually the true beginning point).
For the most part, in this discussion I have been using the term "downbeat" in the latter context. I'm not saying that 3 is the downbeat of the measure. 1 is by definition always the downbeat, regardless of the musical accents, and regardless of which beat may be perceived as the "strong" beat.
When I say "downbeat of 3", I am describing the initial point in time when beat 3 is struck, to discern it from the duration of beat 3.
In International we say continue to rise on two and three then lower at the end of three. We hold the sway all the way through three not straightening untill we move into the next veriation.
Just to clarify, this is not an American vs. Int'l issue, since both styles use the same exact technique of movement. Footwork, rise & fall, sway, etc all work exactly the same in both styles. So with that out of the way...
The Alex Moore / ISTD description of sway is extremely oversimplified, ommitting not just the subtle nuances, but very important aspects of the timing which completely change the movement if interpreted literally. If I was forced to describe sway in such simple terms as one direction per step, then I'd agree with the ISTD -- straight, left, left (or straight, right, right). But the timing of sway is far more subtle, and so I think it's very misleading to oversimplify it the way they do. A more accurate way to describe sway would probably be similar to how they describe the rise & fall... "Commence on the end of 1, continue (or increase) through 2 and 3, and dissolve on the end of 3".
Now the description "end of" is also quite misleading. The common misconception is that it means the literal end of the time span -- that last fraction of a millisecond of the beat. In fact, "end of" is meant to be the later part of the beat -- nothing specifically measured, but for the sake of argument, we can probably say the second half of the time span, or everything from the "and" of 3 to the beginning of the next 1. That's the way the writers of the technique book intended it.
Of course, the writers' interpretation may not be entirely accurate, either. It's probably closer to the truth to say that the rise (and consequently the sway, which very closely coincindes with rise & fall) reaches its maximum on the downbeat of 3, and begins to dissolve throughout the entire remainder of the beat (although it may not be enough to become apparent to an observer until about half-way through).
In the end, here's what we know: When the moment of the downbeat of 1 occurs, we want to be both fully lowered and fully straightened. Prior to that, on the downbeat of 3, we were at the peak of our rise and at maximum sway. Somewhere in the interim, we must lower and dissolve the sway. The entire span of time is one beat. The longer you hold this position after the moment of the downbeat, the less time you have to complete the action, and the more abrupt it becomes. A smooth and graceful lowering and dissolve of sway needs at least half a beat, if not more, at Slow Waltz tempo.
Some may argue that the duration of lowering and dissolve of sway is closer to half a beat, while others (myself included) might prefer to think of it as closer to a full beat, or maybe somewhere in between. I imagine that's more a matter of our individual interpretations of what we think we're seeing, because we're all probably striving to do about the same thing. However, you can't really argue that the sway should be held throughout the entire duation of the beat. If you do, you're saying that the next count 1 begins in a swayed position. That's not just contrary to the book technique, it's awkward.
Regards,
Jonathan