I think everyone in this thread, and the FAA and Boeing, are actually in heated agreement on what V1 should mean operationally: A decision to stop must have been initiated (past tense) at or before V1, otherwise you must continue. So if the toes hit the brakes at the same time as reaching V1, you can continue to stop even though you've reached V1 (and, on my reading of the FAA and Boeing words, even if you exceed V1 during the stopping action, provided the stopping action was initiated at or before V1).
The definition in CAO 20.7.1B seems the one that's out of step.
However, in fairness to the CAO and as I noted above, the FAA and Boeing words don't seem to rule out the possibility of exceeding V1 but continuing stopping, providing the stopping action was initiated at or before V1. So maybe there is the potential for (another) decision to be made at V1. What happens if your stopping action was initiated at or before V1, but fails? Your toes hit the brakes but they fail and have no effect. Wouldn't you have another decision to make? To 'un-make' your decision to stop?