You don't state the type, but from reference to engine start lever I am guessing B737.
V2 allows 15 degrees angle of bank, so no additive required unless the emergency turn specifies a greater bank angle.
From memory, Boeing don't require additive to V2 for icing, though some types may require up to 15 knots! Perhaps your performance analysis automatically recomputes V speeds if you key in icing conditions?
As mentioned, Boeing also recommend that if you have achieved a speed greater than V2 when the engine fails, it is acceptable to maintain the higher speed. In any case the climb at or above V2 is to be continued until the emergency turn is complete, even if this results in an altitude greater than minimum for acceleration and flap retract. In other words, even if acceleration is, say 800 feet, and you reach it while you are still turning you do NOT attempt to accelerate at that point. Complete the turn first.
As for buggering around with shutting the engine down in the turn and still at 400 feet, that's for you to sort with your Company SOP. Where I come from we don't commence the fire drill until at least 800 feet. And only for a fire, not any other failure - we leave other failures, even severe vibration - until after flap retract and MCT has been selected.
In the case of fire, the decision of when it is safe to shut it down rests solely with the PIC, and that would not be while hand flying a turn at V2 !
Another consideration with an engine fire is that usually the engine will still be producing useful thrust, which is helping you get away from the ground . Even in the unlikely event that the engine thrust fails totally (e.g. core seizure) and is accompanied instantaneously by a fire warning, the shut down is secondary to controlling the aircraft and clearing obstacles. But I know from your original post that I am preaching to the converted......
Sure, given enough time you can hone a pilot's skills in the simulator to maintain V2 in a perfect 15 degree banked turn, while identifying and monitoring the shut down, but if it happened for real out on the line three or four months later, I would not want to try it down at 400 feet on a dark and dirty night.