The best way to deal with an engine failure is to not have the engine fail in the first place. Around 80 % of engine failures in light single engine aircraft are caused by the actions or inactions of the pilot.
It is the boring unsexy cockpit and flight disciplines of a good pilot that will likely prevent the requirement to do the hero aviating.....
With respect to the EFATO, yes, nose down immediately has to be the automatic response. I get my students to call out the immediate action drills for engine failure before every takeoff. This always started with
"stick forward" and I wanted the student to physically move the wheel/stick forward to build that automatic muscle memory.
With respect the turn back....well AOPA did a review of EFATO fatals and determined that you were 8 times more likely to have fataliies if the aircraft was turned back to the runway below 1000 feet AGL, over taking your lumps straight ahead