Unpopular opinion but I don’t think it’s fair to ask SQ to provide this to 2 additional people, given that they are not even on the same flight.

Now to the point. If your intention is to minimise walking, and clear immigration together, then check the gate which the Scoot flight is leaving from.

C gates, then use the common business/first check in, located at the middle of T3.

D gates, then use the first class check in at T2.

The T3 first facility is meant to give easy access to the TPR, means it’s only convenient for the A gates.