"he idea with the broom handle is to show that the shoulders remain square.to each other."
Okay, but that says nothing about the shoulders with respect to the hips.
It is true tha many beginners spend years trying to use their arms as handles to torque their body, and as ar esult break their shoulders. The broomstick might help with that. But serious dancers have moved past that error - the alignment of their shoulders is perfectly extended by their forearms, so the broomstick does nothing for them.
"If you go in with a left side lead you will miss the CBM. on step one completely."
Indeed, there seem to be two views amongst world class coaches:
1) Reverse turns do not actually have any CBM at all - the rotation is entirely saved for the second step, at which point it cannot technically be called CBM.
2) Reverse turn CBM is in the hips and feet alone and does not affect the shoulders
"As I say if you can keep your shoulder still and turn your hips you have a distressed look about your shoulder line."
No you don't, because the shoulder line is completely unaltered by the turning of the hips. If it were altered, then obviously you have not managed to hold your shoulder line "still". So your argument is rather silly.
"At the end of the Feather on the count of four and there is a collection point and the shoulders will be square over the hips just as they were in the beginning."
In a word, no. That is not how it is actually done.
"You said about lessons with the worlds best teachers. Can you name me one who doesn't change there shape at the end of the fourth beat and name me even one who teaches a left shoulder lead onto the first step of the Reverse Turn which completely misses CBM on that step."
I do not name names, but of the numerous world-champion-class teachers I have studied with or seen teach, none have expressed an opinion about this other than one of the two I posted above - there is either no CBM on reverse turns, or the CBM is only in the hips.
"To go back to the beginning. Are you really serious when you say to keep the left side lead stiil and turn your hips into it anti - clock."
Exactly.
"This is such Basic stuff its frightening to think you are let loose."
The truth about the basics is rather shocking, when you discover that it doesn't match what your provinical teachers have been promoting...
"If anybody finds this a bit confusing I would suggest you go to the Learning Centre and find your way to the Feather Step."
We are talking about a level of dancing you are not likely to see reflected there.
"Surely nobody believes that there is a right shoulder lead into the Natural."
Natural and reverse CBM are not mirror images of each other. That is the whole point! Natural actions have the shoulders turning first, reverse actions have the legs and hips turning first.
"The class of teacher you are refering to I doubt if you could get a booking."
That just proves your ignorance. Anyone can - but you obviously haven't tried. Yes, you need to pre-plan to match their schedules, but it is not that difficult.