Mike, those are all good suggestions and actually reflect how we train in class to a large extent, experimentation followed by physical and verbal feedback (from Neil and from other people in the group). As for tossing out the "martial application" side, this video was never intended to demonstrate applied or "martial" waza. Both are explorations of movement with a partner, the second is more like applied waza, but it still a teaching technique for the most part.
I take it as a given that you effect kuzushi in some manner (it's a separate discussion in itself), respond, turn, pivot, or whatever... there are a number of factors. Ultimately let's say that you look at the part where you effect the "throw". I could say (for the sake of discussion) that in the first throw you did technique, leverage, etc., and in your Aunkai-appearing attempt you did something else that was "easier" and somehow different. So just looking at that isolated part (you can see how all the rest murked up the discussion) of a "normal" versus a "Aunkai"-related throw, my question would be why that part is effective and I'd say let's break it down. If we can break it down an analyse that small part so that it's understood and then work to improve that aspect, we can ramp back up to the "martial application" level and then (hopefully) have the most effect utilization of I.S. skills in the technique.
In my opinion, jumping too quickly into the most "martial" application tends to leave people with bad habits that are difficult to correct later on.
Take a pole-shake with a white-waxwood pole as an example. In a way it is a simple "application" and I've seen a lot of people say they were doing a pole shake with "internal strength" (often some pretty strong shakes, too, which would certainly be martially applicable, if need be). Yet in many/most cases you can see that in rushing for the results (read "technique") a lot of the other factors like dantien, suit, etc., got left out. The way to analyse and correct is (IMO) to look at the exact moment of application and analyse at that one point, not cloud the issue with everything else or, worse yet, add in an attack by a partner to further cloud the issue. If you see what I mean.