When I was a QFI at the (then) ADF Helo School in Canberra, we used to teach the students combinations of cyclic and collective movements to enter auto dependent on the circumstances, and each to an EOL in a AS350BA.
The most fun one was 50ftAO at 100kts when we wound back the throttle. Initial action was to freeze collective and flare to the nose was about 10NU and we would shoot skywards up to about 250ft (the theory being to get as much height as you can to find a good place to park). After the att was NU, we slowly reduced the collective to maintain the Nr. At 70kts, lower att (lever fully down by now) to adopt normal 65 kt auto att. Nr horn would blare as the anti flare from the non violent bunt lowered the Nr, but approaching 150ft, first bite into flare and Nr would come up nicely, horn would silence, and into normal flare to land.
Another type of LL auto would be a level one at 50ft when you flared to maintain height and used lever for Nr control then final hook into flare to land.
For normal cruise flight auto entries, normally lever down slowly and att raise to get the Nr back into the green, then when flying again, look around for pad. At auto spd att adjust and manoeuvre as reqd.
I don't think you can be prescriptive one way or the other but depends ont eh circumstances.
I think the priority should be to control and contain the emergency and (in this case get the Nr back up into the green however you can, combination of both lever and cyclic) then look around for options (safe flight in auto going somewhere you want).
I have found all these posts quite fascinating as it shows that, even after all these years of flying helicopters, there are so many different opinions as to how to do it correctly. Sometimes there are many wasy to skin a cat.