Before arriving at the correct manoeuvre, you need to be aware of the conditions under which the engine is lost. As Geoff has said, the intervention time will vary with the conditions of the failure.
For a manoeuvre with an expected failure and where the indication are clearly annunciated - i.e. at TDP and with a good audio warning (a voice for example); intervention time can be as low as 0.5 seconds (which is permitted in CAT A design). For a failure that occurs in an extended hover, the intervention time is likely to be more than this.
For an aircraft performing hoisting under HEC Class D; there is almost no penalty for an engine failure and the aircraft will not loose more than 10% of the line length or 4ft whichever is the least. For a heavily loaded aircraft performing hoisting under rescue (or aerial work) conditions the drop down is likely to be conditional upon the engine control system (a FADEC system is always preferable to a hydro-mechanical system), the mass and the environmental conditions (including wind).
When the HAPS manoeuvres were being modelled, simulating an engine failure at RP (TDP) with a 1 second intervention time showed that a rotation 'through' 20 degrees provided the least drop down when the wind was below 5 knots. With the wind at or above 20 kts, a 20 degree rotation would add about 50ft to the drop down.
Modelling the optimum rotation showed that a linear reduction from 20 degrees (for a five kt wind) to about 5 degrees (for a 20 kt wind) would optimise the drop down (and have little effect on deck-edge clearance).
Any procedure that is put into the Flight Manual has to be clear and simple; for that reason, you are unlikely to see a graduated rotation with any published procedure. (The CAT a procedures also have be tested under low wind conditions (the most demanding) which leads to a single (published) rotation figure.)
With a take-off procedure that can lead to a drop down below deck height, the first part of the procedure is optimised for deck-edge clearance and little or no benefit is (can be) taken for wind effect. Wind accountability is usually only provided once the initial part of the manoeuvre is completed.
More if you wish later.
Jim