that link does not work for me.
I have seen people take off rope halters AFTER the bridle is totally on (except for the noseband tightend)
put rope halter on normal way.
put bridle on right over it, even putting bit into horse's mouth.
undo rope halter from the top , as normal.
let it drop down. The bit will prevent you from being able to take it off.
take the nose portion down below the nose/lips and lift it up INTO the horse's mouth and up and over the bit, which is also inside the mouth. It will come out the other side, the side of the mouth which is part of the lower jaw. Hores will kind of spit it out.
Now you can pull the whole thing away from his head
This is one of the Parelli excersizes. I think it's a lot of bother, but it does teach the horse to accept you putting your hands and all kinds of things into his mouth.