An excellent summation of the complex system and thank you for it !
As I can remember from the J32, there was one switch for the APR which, with both airlines for which I have had the doubtful pleasure of flying that not very aerodynamic wings goblin, was usually disconnected. As a matter of the fact, i do not remember that APR use figured much an any checklist . I cannot also remember whether APR was fitted on the original Astazu engined J31 - at least one was still flying from Cranfield quite recently.
Be such as it may, there is an article in today's Star newspaper which says that the SA CAA and the UK AIB are more or less saying that pilot error was the cause of the crash and that the operating engine suffereed a sudden loss of power. The article also says that ATC quite correctly informed the cockpit as to the engine that was smoking on rotation.
It will be seen in the future what any full results may be and it appears that no one had yet spoken (officially anyway) to the pilots who are still not well.
However-if pilot error is proved in this case -there would seem to be errors made in principle in regard to EFATO handling on that type of performance aircraft.
A shame and a worry for all concerned but I repeat the maxim-at the great risk of being shot down-do nothing until 400ft except silence the fire bell; segment climbs and all that stuff, which do not really apply to light twins but do apply to the category of aircraft in which the J41 finds itself.