I guess I'm a semi-believer as I think there is still something missing. The following quote I think points us to where there is a problem in the assumptions.

"Another way of looking at it- if you were able to make your body completely rigid and affix your feet to the bottom hull, there would be no need for the righting line (essentially make yourself a cantilever beam). "

I agree with this statement. The problem is that in reality we can't rigidly affix our feet to the hull and thus our feet cannot apply leverage or righting force to the hull and the righting force must be transmitted through the line. While it may not make much difference whether the line is tied at the top beam or over the top hull, as you progressively lower the tie point it seems you will eventually reach a point where your inability to be a "fixed cantilever beam" will prevent righting of the boat. I don't know where that point is but if line position didn't matter everyone would tie off at the bottom beam where it is easier to reach? Since I can't fully grasp all the physics involved, I'm going to have to do some experiments with my cat in a calm lagoon this spring and see it for myself.