"Coming into the the Reverse Turn, the lady must move out of the mans way. Not like Alex Moore's book which has the lady still holding a diagnal to the centre position. Somebody is already thinking how does the lady move out of the way . She invites the man through on the Feather Step doesn't she, and she should also on the first step of the Reverse."
This is the thinking of someone who hasn't learned to do actual CBM... you that problem often, and at suprisingly high levels.
The lady can invite the man forward without getting off her original diag center direction of movement. The post even has the clue to how - she manages it just fine in the feather without stepping off the track (if there is any curve in the feather, it's between 2 and 3, same as the only place where there's curve in a reverse turn)
If you do actual CBM, which involves rotating your body until is it no longer aligned with your direction of movement, you will not have any problem making space for your partner when commencing a turn, without needing to step to the side of their path. But it will take about a week of practice to break some lifelong (pre-dance) habits before you can isolate your body parts and recordinate them in this way.
"I'll quote Anne Lewis here. BEFORE the first step of the Reverse she turns her hip towards the next alignment and does not worry about where the first step, which is backwards is placed."
Exactly - the body turns quite early. But be carefull, the direction of the step is backwards relative to the standing foot that you are departing, which is to say in the same direction in which the preceding step 3 moved. That consistent direction of motion will NOT BE BACKWARDS RELATIVE TO THE ALREADY ROTATED BODY, BUT RATHER ALMOST SIDEWAYS. Many make the mistake of curving their step to match their body rotation. If you isolate you legs and allow them to simply continue in the direction determined by your momentum, they will end up fine just as Anne suggested.
On Moore: yes, posture has evolved, but the goals of the modern dances have not. We try to do more today, but we still need the underlying details worked out so long ago. For latin things are different - those dances were only in process of being adopted to the ballroom at the time the classic authors were writing, and as a result what was written about those has not stood the test of time nearly as well.