That said, if I wasnt climb gradient limited I would certainly be happier at V2 + 10 to V2 + 20 as my particular plane isnt very nice at V2.
In the old days if an engine failure occurred beyond V2, the technique was to pitch up if necessary to revert to V2. This was because the obstacle clearance gradient was based upon climbing at V2 following an engine failure.
This policy was changed after an American Airlines DC-10 crashed shortly after take off from Paris. Briefly, a wing engine fell off its pylon shortly after lift off. As the aircraft was accelerating, the crew did not know initially the engine had gone. Damage was caused to the leading edge slats on that side causing them to retract while the slats on the other wing remained extended.
At the speed the DC10 had reached shortly after the engine fell off, the aircraft was controllable even with its slats on that side coming in due loss of hydraulics. . However, when the crew reduced the speed back to a V2 as per company policy at the time, and the left wing slats fully retracted, the crew were unable to maintain wings level. The aircraft rolled almost inverted and crashed. See report:
Lessons Learned
Later flight tests revealed there was negligible loss of climb gradient between climbing at V2 and climbing up to V2 plus 25 knots. Thus if the crew of the DC10 had climbed at the same speed it had attained after the engine fell off the wing, controllability could have been maintained and the accident averted. Manufacturers amended their AFM accordingly.