Phone VFF up would be the best way.
Or transfer points from VFF to KF and phone KF up to make a booking.
Or if you do not want to go through SIN ICA, do the transfer on the inside, with a paper BP from the people at the transfer desk.
Depending on your dep schedule of course.
SIN Changi is very easy to connect, without having to go through SIN immi.
They have transfer desk inside the secure zone of the airport.
You can do OLCI with SQ.
MEL has a very first dep with SQ at a bit after midnight, giving you time to get a midday or afternoon flight to some Indian airports.
SYD has a curfew, so first dep would have to be at dawn, getting to SIN a bit after lunch.
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On a sidenote, the A350 that SQ fly from SIN to airports in India, do not have a premY, and only one of their A350 from MEL has a premY, but their B777 do have a premY.
So phoning up would be the only way to get a reward seat booking, with mixed classes.