Hi OPEN DES,
Too many questions for me to answer straight off but a couple of thoughts:
However for G/A we allow AEO thr reduction/accel alt routinely to be below our minimum G/A EOAA (MSA/missed app alt). Surely once thrust is reduced and or acceleration has begun we are commited to the AEO scenario. What if the engine fails at this moment?
1) You do many take offs, but few GAs, therefore the chance of an engine failure during the GA is much less than during the take off.
2) If you suffer an engine failure after AA on the GA, then your all engine climb out would have been much bigger than the minimum required gradient.
3) We have the luxury of being able to choose nearest "suitable diversion airfield" after an engine failure - so choose wisely.