Been facing the same conundrum recently, as we're planning a family trip to Europe this time next year, so have been watching the daily award release closely for various city pairs over the last fortnight.
I've been looking ex-MEL rather than SYD but I see the same pattern: all the MEL-SIN saver award space for a given day gets released at 10am, up to a day ahead of most of the connecting SIN-EU space. I would have assumed married segments came in to play but I've seen a consistent pattern where if the AU-SIN leg you want has already gone to waitlist by the time the onward connection opens (presumably because someone booked it), then the AU-SIN-EU flight with that sector in it also goes to waitlist immediately on opening up.
Depending on where exactly you are heading, some destinations do seem to have both legs opening together -- I think it depends on the exact time that the onward leg departs SIN. E.g., I was looking at MEL-SIN-LHR as an option, and there's SQ248 (the 05:55 departure -- ouch!) that seems to open up in the 10am release at the same time as the corresponding connecting flight out of SIN (SQ318). It wouldn't be my first choice, but that one at least seems to be bookable before anyone has had a chance to nab either of the sectors.
I'm not sure there is a good strategy -- apart from a bit of minor flexibility on dates, crossed fingers, and being ready to book bang on 10am?
(It is do-able though--successfully bagged 4x J savers MEL-SIN-MAN this morning despite the twin challenges of only one SIN-MAN flight per day and the MEL-SIN legs having opened up yesterday and been available to book separately for 24 hours).