The guy from SQ didn't seem to know anything... "Raffles business class" is meaningless, there hasn't been a "Raffles Class" for a few years now. Fully flat beds are available only 77W/A380, which you can't book using award miles. The best you could get is a SpaceBed, which is a non-fully-flat bed on some 777s and 747s, but as said, these aircraft are usually not operated on SIN-NRT.

I'll throw in a third option: fly OZ via ICN. Last I checked, OZ's SIN-ICN flights are overnight and always have SpaceBed-type inclined flat beds in business, and ICN-NRT is a very short hop where regional J is no big deal. Service isn't quite as stellar as SQ/NH, but it's not bad either and, if you're like me, on overnight flights it's the bed that matters. You will have a change of planes in ICN though.