use (or used to when I did this stuff) the "dark and stormy night" test - could I do this myself in the aeroplane on a dark and stormy night having just flown 4 busy days, am totally shagged, and have an ineffective offsider
The chances of that combination AND a engine failure at V1 AND the lowest worst flight path gradient, is for all practical purposes, zero. We fly complicated SIDS with one engine inoperative provided the info provided by the performance engineers is correct. This includes dark nights and long duty hours. Of course these are assiduously practiced in the simulator and any totally shagged pilot given further training.
What pilots need to know is to what distance from the runway is the obstacle survey valid. I flew with one well known European 737 operator who provided individual runway analysis charts that only went out to 5 miles and then you were on your own with a vengeance. The excuse given was the particular country that provided the obstacle charts only measured out to 5 miles. As there was a bloody great island with a hill 2000 ft high just 7 miles in the middle of the engine-out flight path, this was not mentioned.
All runway analysis charts that take into account obstacles should include where pertinent an "escape" procedure with sufficient guidance to enable the aircraft to reach a safe height for return for a published instrument approach.