Fine or coarse propeller pitch
FWIW, if I was going to do trouble checks following an engine failure, I'd put the propeller to maximum rpm (fine pitch). Once I had decided the donk wasn't going to restart, I would consider minimising drag by pulling the propeller lever fully aft (coarse or feather).
However, I suppose a particular manufacturer might say "in the event of engine failure, push propeller lever fully forwards" or similar, which might be why your CPL instructor did not explore the coarse propeller setting.
Alternatively, if a SE aircraft suffers a loss of oil pressure, it may not be possible to get the propeller out of fine pitch anyway due to the construction of the CSU.
HFD - is the SLA technique of RAF origin, or is it universally used in the UK?