oldebloke,
Yup, up to a point I agree with you, you might possibly get away with a continued OEI Takeoff from V1-10 and tolerating a much reduced screen height, but what concerns me is that the screen jeight might be zero, that is, you haven't yet become airborne at all. The acceleration from Vef to Vr and V2 is a massive performance demand for any aircraft, particularly the 2 engined aircraft. Nevertheless, the GO decision in these 'odd-ball' circumstances is probably the lesser of 2 evils.
All of these discussions, of course, relate to engine failure, other events such as tyre/tire failure are clear cut GO cases.
If I can harp on about the lower V1's that we accept with a lower screen height for Wet runway cases, it must be remembered that this performance is based upon a lower Takeoff Weight limit, and to apply Wet runway data and procedures to a Takeoff at the higher weights permissible for a Dry runway is very risky business.
rhovsquared,
You make good points, but in FAR25 (and it's equivalents) aircraft rarely operate to the WAT limit, takeoff is usually limited by Accelerate-Stop and/or Obstacle clearance. Certainly, for an aircraft such as the B737 operating from excessively long (say, 3,000M/10,000 ft plus) runways, WAT will probably be the limiting factor, and 'messing with the speeds a bit' probably wouldn't do any harm, no guarantees. Similarly, if the aircraft is meeting the minimum OEI 2nd segment gradients, but no obstacles exist (e.g. over water), then again, you'll probably get away with it, again, no guarantees.
A historian once said that given the choice of living your life with Adolf Hitler or Josef Stalin, you would be living in great danger in either case, but more likely to survive your time with Adolf Hitler. I think that Herr Hitler would favour the GO case from V1-10, and that's about the only time that I'd agree with him.
Regards,
Old Smokey