Nicholas it's not the AoA that we need to reduce, that'll be the same for a given airspeed (V2 in this case) regardless of the number of working engines. We need to reduce the angle of climb to ensure that we can maintain the correct airspeed.
I can't answer your question about the certification process but suffice to say that an aeroplane will not climb at the same angle on one engine as it would on two. For instance, the usual climb angle, initially, would be round about 15-20 degrees, for a single engine case you'd be looking at about 5 degrees to maintain your airspeed. If we try and climb at the normal angle then the airspeed will quite quickly reduce to and below V2 (assuming we did nothing about it) and then you will find yourself in all sorts of bother.
Edit: In the case of a failure at V1 or Vr it is essentially the same process. V1 would be the worst case as it is the lower airspeed and would require a greater rudder input. However, generally there is very little difference between the two speeds (although I have seen a difference of 25kts between the two speeds). If you have an engine failure at V1 then you control the aircraft with the rudder and continue to accelerate on the runway to Vr before you rotate.