Genghis, a challenging project.
There appears to be two main aspects; a quantitative analysis of aircraft performance, using definable variables.
Then there is a qualitative part relating to human performance; you seek to 'fix' this with a recognition time. For a theoretical analysis a representative value can be chosen - an assumption.
However, any practical analysis would depend on further assumptions.
Given engine failure recognition (establishing safe flight), there would be a further decision to turn-back or not. This requires different, wider understanding, with significant demand on sense-making and delay before manoeuvring.
Recalling my basic military training - never, ever turn-back; greater experience questioned when would a turn-back situation become a forced landing at the departure airfield. An astute instructor answered this by declaring IMC, requiring ejecting.
Another recollection; a reputable regulator posed a special condition on a multi-engine commercial aircraft, to demonstrate an all-engines inoperative landing - any event encountered in their country. A mix of flight demonstration with reduced power and piloted simulation defined the performance boundary in order to reach an airport. Discussing the approach and landing, the aircraft was capable, the tp declined further tests on the basis that the outcome would be so subjective it was meaningless.
Finally - James Reason; what ever assumption you choose, it will invariably be wrong.
Good luck.