You do know that you get no miles on most FFP in "S" class, don't you?

Most likely "S" class has limited number of seats for sale ex-SIN. Expertflyer and other search engines only display certain availability seats, and not actual-time availability seats called Direct Access. So the seat may seem to be available in everyone's systems including CX's online booking because they use itn availability and not their own search engines, funnily enough.

Try and call CX in SIN directly and see if you can book through them. Sometimes CX restricts POS and you get the error message. But upon checking CX's Direct Access, those flights are all available in "S" class both ways.