Your route is one of the most popular ones to Europe. Last minute Suites or First availability in general though is very challenging in my book. I have been on waitlist (saver award to be fair) even before Covid when there were still 12 Suites on A380 and the flight left with empty seats upfront (I had backup booking in Biz so could see the load).

So don't be surprised if SQ rather leaves seats empty especially in Suites/ First and to a degree even Biz than make them available for last minute redemptions. They will always take cash of course, be it outright upfare or via the upgrade bid (fixed price offer at the moment). Maybe Advantage award may pop up last minute, but Saver I would declare the chances extremely low unless maybe a route like CGK, HKG or such short flights. Being TPP or at least QPP should help as well.