How are you going to convince ATC that you can fly IFR in controlled airspace. They do not expect twin engined aircraft to change flight levels in the event of a single engined failure. Increased range in any sort of breeze only works if you are flying downwind.
The only time I have known, in helicopters, for a deliberate single engined leg was where the destination and the diversion had socked in and it was a case of just about making it to somewhere where they could land.
Somebody was demonstrating the single engined performance of the Wessex. Easy, look, you can winch with one engine; then the good engine ran down. The bloke on the end of the winch only just got away with it.
'power saving mode'.. Most large twin's engines are running at 50% power in the cruise. The idea on using one engine is because at 50% power they are using 60% of the fuel that they would use at 100% power.