I once had to ferry a Puma "single engine" from an oiled sand strip on a Caribbean island. The other engine refused to start despite the efforts of some of our ground crew/engine mechs on scene.
We used the normal running takeoff departure technique, basically as described above. That was uneventful because we regularly practiced them. I was actually rather more concerned about the over water flight that followed because we were the only available local SAR cover!.