But it ended up with an overrun....
The weird thing is that when I look at the video and the other materials, it seems to me that the overarching concern is RTOs that ended up with overruns but would not have if the take-off had instead been continued. And I keep giving scenarios in which the aircraft is over V1 and I just keep getting told "continue stopping" or "you're on your own" but not a third (and to a layperson like me - obvious) option.
I note the definition quoted by LeadSled does not prohibit the un-making of an RTO decision. That definition only says in effect that you must continue the take-off if you haven't initiated stopping at or before V1. It does not say that you must not continue the take-off even if you exceed V1 after initiating stopping action.
"You're over V1: You must continue the take-off!" Got it.
"You're over V1: You must continue to reject!" WTF?
That's why it seems to me to boil down to the spool up and spool down times of 'modern' engines. However, this may turn out to be a theoretical rather than practical point.