Pronouns & antecedents? I think that I would just concentrate on question marks for now. We Social Dancers can spell and write grammatically, but it's not everyone that can.

Don,(AKA Polished)

You wrote:
/* I'm with Humpty Dumpty who says that man should rule the words and not the words rule the man.*/

I thought he was more famous for saying, "Don't push me, man!"

"Surely the restoring force going up would be in the same direction as on going down (like in a bob) but in this case we need to to generate horizontal movement in one direction (not back and fourth like in a bob)."

Simply imagine that at the top of the swing, the original pendulum string is abandoned and replaced by a new one, anchored on the ceiling further down the room. If the swing rises to the point where the movement has fully stopped, a downswing in any direction is equally possible (pretty much only the LOD convention keeps us from lowering in waltz back in the direction we came, but it can be a good choice at times). If a small amount of residual horizontal movement is maintained at the top, then lowering in a direction that utilizes that makes sense.

"The Double Reverse Spin is used in all three of the Swing dances and requires Verticle lowering. That would include being down at the beginning as well as the end. If in the Foxtrot the step before was a Feather. I would be inclined to lower vertical Lest the partner gets push onto the heel turn."

Ouch!

I'm rather glad I will never have to dance with you, as that would be a very unkind, and likely painful distortion of a feather step. A feather followed by a heel turn in quite ordinary in foxtrot. That the heel turn becomes a double reverse will not require any modification to the preceding feather. Any attempt to lower vertically from the feather would quite destroy it!

"This is how the man is able to go past the lady on the third step of a Feather"

Only an pushy, ignorant man would ever want to. A DANCER in contrast knows that outside partner position is danced without letting the bodies slip past each other. Only the foot is outside, while the lady's body remains in front of the man's. You can especially see this in the position of her right hip, still soundly in front of his. Their upper bodies may stretch past each other, but that's not the same thing as passing each other at all.