The notion of transcontextuality doesn't mean something is without context, but rather how contexts are interdependent and as many as possible need to be considered. In fact, that is one of her criticisms, that when we take something out of context like isolating it in a scientific setting then it loses its transcontextual meaning.
This also relates to it being a non-linear process, one that doesn't move through a strictly abstract process of rules like some computer algorithm or classical logical steps leading from premises to a conclusion. That "if you go into it with a goal in mind, you’ve already truncated your complexity." It's not "a map on the wall or a structure or new jargon." It's a mutual learning in "symmathesy."
Going along with the warm data process, each group exploration, while perhaps following a general outline of naming and exploring the different contexts, ends with a new and different symmathesy, even if the same topic is chosen on different occasions. I'm reminded of what Zak Stein said in his essay on the mind as ecology metaphor:
"Ecosystems are composed of a wide variety of independent and yet co-evolving species, so there is not one central 'unit' that can serve as an overall measure of the ecosystem. Rather, to understand an ecosystem you must take multiple measurements in a variety of places across a variety of time scales. [...] No two ecosystems are the same. Every ecosystem is unique. Give two ecosystems the same input and you should not expect the same output."
I also appreciate the improvisational jazz metaphor. As a long-time partner dancer I have that experience frequently. Even with the same partner and the same song, each performance is never exactly the same given all the different interactive elements in that particular moment. Ironically it takes a LOT of training over a length of time to have the tools and techniques of musical and dance structure to play within them yet get creative with them.
However in the warm data process no special training is necessary. It's just people engaging the process and something new comes out of it. In that sense perhaps the training necessary might be already inherent to basic language and communication skills that we take for granted as the shared cultural backdrop, like Habermas' lifeworld? But beyond that maybe nothing more is needed to engage the process? Just riffing here. Someone else take the lead now.