rustle your maths looks ok to me .
There is a difference with practise and real. The ability to bring the "dead" engine up to sort things out is always there.
The ATZ wouldn't figure in my cunning plan. In the works machine we are never in it until on finals.
And if there was a runway within 10 degrees and 4 miles away ahead I sure as hell wouldn't be doing a single engine circuit if it was a real one.
BTW our standard emergency procedure for airports without terrain issues is straight ahead to 1700ft agl accelerate then a 20-25deg turn back to the locator Which we wouldn't start until over 150knts with a Vyse of 120knts and by that point the power would have come back to about 65-70% torque which would have brought the Vmca down by 30% from an initial value of 101knts so we have a safety factor of 2 before starting the turn. Our Vrotate speeds are limited by Vmca until we are only a couple of 100kg off MTOW.