If you tried it after arriving in Tokyo, there's an excellent chance that the agent would spend half an hour on the phone with the help desk before smiling sadly and telling you that yes, it was impossible. You'd have to retroactively re-fare a flight you'd already taken on a partner airline. I think it's possible, in the same way that it's possible to cut a suburban lawn with scissors, but finding someone with the requisite skill and willingness to try is a crapshoot at best. It's not the way that I'd want to spend my layover in Tokyo. (There's also no guarantee that R space that you see today will still be there by the day of the flight).

Barring IRROPS, in which case you might end up in W+ just by serendipitous chance, this is something that needs to be done before you leave SIN. And you can't waitlist a GPU within 24 hours of departure -- you'd need open R space at the time of application. Throwing in the SDC is going to make things tricky. I would suggest just changing to the flights you actually want ahead of time, assuming that there is both W and R availability, but the chances of getting the change fee waived drop precipitously if you're changing the flights too.