Well, we got ourselves into a nice little discussion here. I perfectly got BOAC's point, so I suggest ourselves to discuss the "most critical" part in an engine-out takeoff.
I would say the 2nd segment (2.4% CLB requirement) would be the most restrictive part of the whole engine-out procedure or SID. Should an engine failure occur after the second segment, I think it would be feasible for an airplane to continue the (regular) SID for a return to the departure airport, and I'd say it would be an option to consider, IF safe means to fly the company procedure are no longer, well...safe
I am well aware of the infinite combinations of factors that could make this statement easier or harder to be accomplished in real life; but I stand to be corrected.
Best regards