I would suggest what we teach is the same as in the UK....When the Engine quits for real....go for the best possible landing site...be it the Runway, Taxiway, Roadway, or cornfield.
Practice EOL's are not Emergency Landings following an Engine Failure or as in this case a Throttle system failure....thus one could give preference to other landing places than the Airfield's active Runway while doing training EOL's.
Picking the Runway was not this Pilot's mistake....initiating the Autorotation too early was...especially after being reminded of the need to be OVER the Runway before doing so.
Thank you for the informative part of your post which confirmed my recollection of the TH-55A (US Army version of the 369)....looking down between your Pedals was how you picked your landing site.