18-Wheeler,
It should come as no surprise that
"the engine failed about two seconds before V1 but kept going and the plane took off just fine",
that's what the aircraft is certified to do!
Certification is based upon Vef (speed of engine failure) being 2 seconds before V1, the intent being to allow for suitable recognition time. (In earlier times it was 1 second, a little unrealistic). So,
18-Wheeler, what you have done is to exactly replicate the certification process, and obviously the test pilot also found it to be "just fine", which is why the aircraft gained it's certification.
Calling V1 5 seconds before actual is a disaster in the making. V1 is a two way speed, you Stop, or you Go. For the Stop case, call it as early as you like, and the Accelerate-Stop performance can only be improved,
but for heaven's sake don't GO!. The continued Takeoff case assumes Engine out acceleration from V1 (Vef actually) to Vr, then to V2. The distance consumed in this manoeuvre is considerable, and some would want to make it longer, but you're limited already, so you crash. Does
stilton's operator calculate the extra Takeoff distance required to accelerate that extra 5 knots with an engine inoperative? With all engines, 5 knots worth of acceleration would be over in the blink of an eye, but with an engine inoperative, perhaps another 1000 Metres or so.............
That's the Performance aspect, but has the control aspect been considered? V1 must not be less than Vmcg (to cover the continued Takeoff case), and, in many instances, V1 does indeed equal Vmcg. Now, someone wants to continue the Takeoff 5 knots below Vmcg, and directional control will be lost. At least the ensuing crash will be within the airport boundaries, making it easier for the fire engines and blood wagons to get to the wreckage.
GET REAL! Fly the aircraft the way it was certified, you're tinkering with very small safety margins. The manufacturer already assumed that it would take you 2 seconds to recognise the engine failure, it's built in to the figures. Don't try to re-invent the wheel.
Regards,
Old Smokey