Until now I'd never really thought much about figured bass notation beyond the basics I'd learned from studying Rameau's wonderful treatise years ago. But thanks to your work and explanation it now appears to me (if you'll forgive my naïveté) that some composers would perhaps have used figured bass notation in order to reach out towards best possible universality, knowing that, as you say, musicians could easily improvise - in apposite ways - their own versions of full arrangements. And dance is perhaps the most universal of all musical genres.
I've no doubt musicians understand very well that we humans are all inclined to be parochial creatures at heart, in that we each tend to favour communications (verbal and non-verbal) couched in our own most familiar idiom. Hence in the case of working from no more than written melody & figured bass, an ensemble of players would naturally and intuitively improvise their arrangements as apposite to the natural idioms and ambiances of the milieux familiar to them in their performances.
Thus I suppose, in principle at least, one dance piece written using the shorthand of one or two lines of melody with figured bass (together with, as you said, a visual representation of the dance's 'configuration'), could be welcomed as warmly and enthusiastically in, say, an 18th century central European aristocrat's salon, as in a 21st century country dance gig somewhere in the North American continent - all depending on what the musicians make of it at the particular time and place. (But I do appreciate that mostly these pieces, as you noted, are already somewhat fitted for particular kinds or 'classes' of milieux.)
For me, fascinating as well as educational thoughts; and I thank you sincerely for that, Jos.
