Not sure how you were taught back, but most good swim coaches are going to have you learn how to nail body position and kick b/f they add in arm action. Trying to add kick timing to the arm stroke is really tough I'm not sure I could coordinate it and swim backstroke that way. The more I think about it I venture to guess I'd be lost if I tried to swim back with arm action as the focus and then add in intricate kick timing. I think this is one reason so many adults find a 6 beat kick so difficult with freestyle. They build their stroke backwards with arm action first and then try to add leg action by fitting them into the stroke cycle.
This drill is so old I was doing it in the 70's and it hasn't changed one bit! If you use the kick to power rotation the shoulder and subsequent arm action will just happen and it becomes just like freestyle in that it's a recovery stroke.
There is a reason you don't see people emulating Ryosuke and his kick technique. He is a 1 in a million with total perfection of his body position and stroke timing grabbing enormous amounts of water. Quite simply he is a freak that can get away with it.
I am not taught, DIY training.
I think you are right that in pronciple its best to start swimming bottom up from a 6 bK with rotational kicks.
Since my kick is crap, but balance good I can get away with little kick.
When starting form balance and using hip and body to rotate at least the main kicks are more or less in place, because rotating the hips automatically happens with a kick supporting that movement.
THats the basic 2BK action.
I have noticed thats not optimal, certainly at lower strokerates.
On the right side, when trying to just get the continuous flutterkick going without much thought and rotating the hips at the same time, the kicks starts to fall in place sometimes.
Its a matter of locking the continous flutterkick rhytm to the 2BK anchor kicks.
It seems at the right side its going to a 6BK. At the left there is still one or 2 kicks missing from a full 6BK.
(The flutterkick has a tendency to stop at the left side when I focus on the anchor kicks)
Sometimes the kick keeps on ticking for a few armstrokes and that is great.
The machine really needs the 6BK to get a nice rhythm it seems.
With very good balance and tight body 2BK is OK ish, but 6BK feels much smoother.
At very high strokerates 2BK could get better, just like in freestyle, but thats no option right now. Taking about 18-20 strokes/25m .
Feeling of traction on the water starts to get better and better.
Start to let the arm slip a bit at the very start of the stroke when getting tired instead of locking the water in right there to not have to haul the body past it because its quite hard on the core to really power through the stroke while keeping the body straigh with minimal fishtailing.
When this sloppiness gets too big its time to take a rest.
Getting/keeping backstroke straight and tight is an insane core workout.