T/O Performance
Note that T/O performance with one engine less, is less than with all engines running.
Performance calculations are only performed up to 1.500 ft Height (above take-off runway). If there is a performance problem, that is, if obstacle clearance is not guaranteed in any direction, then a specific engine-out departure procedure will be developed (by the operator).
If you get an engine failure after the point where the engine out procedure splits off from the ATC SID, first of all note that you are then already at an altitude that belongs to all engine performance up to that point, so greatly above any near obstacle problems. Secondly, now it is up to the captain to determine the safest course of action. Usually this will involve not to continue in the direction that requires the high climb ratio's that you are referring to.
To recap: performance calculations are per runway, not per SID. The performance will be safe omnidirectionally (so, usable for all SID's). If there is a problem in any direction, then a specific engine out procedure will be provided. Obstacles that are distant, like a mountain range at 30 nautical miles from the aerodrome, usually fall outside the scope of take-off performance calculations - they will have to be adressed via the common sense of the flight crew.