I don't think the judo way of doing it is same as the BJJ way of doing it. Totally different details in each of them. In the gogoplata, I feel the overhook is key to getting enough control. You also should have your arms wrapped around the head, grabbing your own foot. then pulling down as your push up with your leg to initiate the choke. I also always do the move from my hip shrimped out a little. In the kagato jime shown, they just hold the gi and press up with with foot. They are all flat on their butts. I don't feel this is as effective. It could work, but I don't like it as much.
I agree, to an extenet.
Us Judo, Euro Judo, Russian, Korean, Japanese all have discicnt styles, not even counting the differences between schools.
There are pics floating around of the exact move done in Judo from the 30's. Grappling has been around for along time, way before Eddie Bravo and Weed.......