And an even better question is "Do we have a noun for a martial arts
stance, so that it can be used as the object of much, to begin with
?".
Yes, martial arts stances are named ending in {tonSaw'} (like how {per yuD} end in {Qu'}).
I will post a transcript of my Q&A with Okrand/Maltz later today, after I've had a chance to look it over for typos and maybe get some clarification on some points.