I had great success with an adult first day skier last weekend as well. I think our students went through a similar progression, but mine was able to do the wedge christie. He didn't want that, he wanted to ski parallel like his buddies. The snow was soft lumpy spring snow, so I decided to give teaching him parallel a try. He was very bored on the beginner slope accessed by the belt, and once he showed me he could do a wedge turn by pivoting both skis around the ankles, I took him up the lift. I promised him we'd get to parallel, but he had to get familiar with wedge turns first with the new slope's gravity and pitch.
He did fine with short wedge turns. Then I had him do wedge christies, which your skier found difficult but my guy did just fine with. We had done wedge change-ups on the belt area before (straight run in a wedge - parallel - wedge - parallel) and he'd done fine with those.
After that I had him carve/slice (parallel skis, edged, no rotation, park and ride) some huge J-turns across the slope cruising uphill to a stop in both directions, and we kept doing that with steeper and steeper initial fall line angles to gain more and more speed. He was finally having fun! This guy was thrilled and totally hooked at this point on skiing. What a blast - for me for me as well as him. We were lucky to have empty slopes -- all the rotating skiers had quit and gone into the bar, as the heavy soft sloppy spring snow wouldn't comply.
I got him to do some Schlopy type drills to introduce angulation so he would stop banking his wedge christies, then I had him do some long linked J-turns that started with a wedge, shifted to a flat-ski-christie high in the turn to gain speed, then finished with a tipped-knee carve/slice through the snow. One massive J-turn in both directions, coasting to a stop uphill each time, keeping that angulation going so the downhill (outside ski) was loaded. He was almost ready for the parallel turns -- and getting down the hill with high speed (for a slow snow day) and having lots of fun. We finished that run linking those long turns. I was amazed he got it, but I think the platform provided by the snow made it easier than it would have been if the snow had been hard.
Next, we went up a higher lift (first time I've ever been able to do this with a first-day skier in a three hour lesson), and I had him do linked short wedge christies, then linked long wedge christies finishing with the carve/slice. We focused on maintaining that angulation to load the outside ski as well. When he was comfortable, I showed him how to replace the wedge initiation with a release: collapse the downhill knee to move the downhill hip down toward the downhill boot beneath it. This description has worked well for me - just move the hip straight down towards the boot - do nothing else. I explained that his shoulders and head would also move downhill, but the point was to move the hip down over the boot and not to worry about anything else. I explained how the ski would turn on its own and demonstrated for him.
He did it! Boy was this guy happy. He linked parallel turns (no rotation in that snow) all the way down to the bottom. We were out of time, but he had a bunch of tasks to work on and enough skills to get him around a bit on the mountain in that spring snow. Plus he had the rotated wedge turn to use should this prove too fast for comfort on harder snow.
This was the best/fastest progression I've had with a first day skier, and I'm ready to try this again with similar skiers on soft snow again. Can't wait to try some version of this on hard (normal) New England man-made snow next season. I don't expect the same success, but I'd like to be wrong.