"Push forward", "EFATO", "Unload" are all rather vague terms for the ab-initio. My first thought is that if you ever have an engine failure in any climb or significant turn (not just after take-off) you will need to react more quickly than if the failure occurs in straight & level flight/descent. However you describe it, you are initially trying to reduce angle of attack and then manage a limited amount of energy by selecting the most favourable AoA. It is the rate of change of energy that causes problems.
As far as turning 30 deg or back, it all depends on your definition of EFATO (ie how high and how close to the airfield you are). There are occasions where a turnback is entirely appropriate; especially if there is a cross runway available and you have enough height. Picking up on a previous post, I think glider pilots are far more attuned to the options in such scenarios, something I have noticed when converting them to SEP.
Anyway, just my tuppence worth.