Given the sort of height to be cleared, I would put my money on stopping performance EVERY time in a crossing situation detected prior to V1 - the risk outcomes warrant avoiding a highspeed impact at all costs ...... there was a celebrated almost disaster at Sydney years ago ... as I recall a domestic 727 was faced with this sort of situation when an international DC8 (?) took a wrong turn and crossed the active in front of the accelerating 727.
Post accident analysis indicated that stopping would have been a doddle. In any event the crew, faced with a situation for which they had no knowledge or training, took a punt and went for the continued takeoff ... the result was that the tail of the 8 ripped the belly out of the 727. The 727 crew then did an excellent job of recovering the situation.
They were, of course, crucified at the enquiry and in subsequent legal proceedings .....