I did not read the whole topic, I am sorry.
I am french and it is very hard for me to understand everything... Be indulgent, please...
But I am agree with some ideas.
For me, the double bridle should be used when the horse is perfect in bridle.
It can be a good aid when the rider and his horse have a good level. It gives delicacy in the requests between them.
The work is more discret and it will be more appreciated.
For the first time, it is better if a teacher helps the rider Especially if the horse starts with the bridle. He can see the errors and correct them.
And the more important, for me, is to do not forget the bridle and work with it as much as possible.