Well I have an up to date Boeing manual which I borrowed. However the EFATO scenario covers a failure at V1. If using a derate and assumed temp it says I can select TOGA after the engine failure select gear up and only after reaching acceleration altitude and flaps up I can select FLTLCH (MAXCON). Aircraft is flown with autothrottle engaged the autothrottle servo on the failed engine is turned off.
However it does not cover the case where climb thrust is engaged and flap is still in the take off config. Hence the query. I believe the old theory of autopilot out, autothrottle out is no longer applicable on the new Boeings.