Thanks, Overrun, and as always a tremendously informative post.
My beef is that there is a big difference between what should be and what is. Supine regulatory oversight, heavier and heavier aircraft, and the shopping mall model of airport management, may or may not contribute to this.
It I were running an airline these days with anything heavier than a large turboprop, I would not rely on the airport operator or the Regulator to ensure that the stopway is properly constructed. If the airport cannot supply well-documented, recent test results, I would have my own tests carried out and adjust the runway distances if necessary for my aircraft, either to avoid the stopway altogether or to reduce the speed at which it would be entered after a max weight rejected take-off at V1.
PS If an intersection is used, it would only be if the ASDA from the intersection is sufficient for that take-off, (plus all the other factors, eg obstructions, are not a problem with the displaced start of roll). So that's alright, then, except that if the full length is used there's lots of spare pavement to pull up in more calmly, probably without even entering the stopway, as opposed to hitting the stopway at "some" speed with full braking, and hoping like hell the undercarriage won't collapse. As someone said in this thread, runway behind you is useless when you're trying to stop.
PS. I have seen a landrover stuck up to its axles in mud, fairly recently, in the stopway of a Cat 6 runway in the UK, after a period of not unusually heavy rain. I rest my case!