If you cancel EWR-SIN, it might not go back to the award inventory. Or it might go to the next one on waitlist, and even if it go back to the award inventory, it might not show up for EWR-SIN-DPS as SQ have different quota.

maybe you can try to waitlist EWR-SIN-DPS.
if you do not have the miles, maybe have to keep on logging to check. It seem like SQ might have release very little award seats for EWR-SIN currently. So they might release more later on.