I've done this one quite a few times and have another upcoming. As CWS says, there's no ideal here. But I'd be looking to get a decent rest on the LHR-SIN leg, and then another few hours sleep on the SIN-SYD.

On the return, just sleeping on the SIN-LHR would do it for me.

As for meals, I'd always have dinner on Leg 1and maybe something light on Leg 2.
Returning I'd eat loads on Leg 3 and sleep it off on Leg 4!

Don't forget the showers in SIN can be a godsend to refresh you in either direction. Take a small change of shirt, underwear in your carry-on. Makes a world of difference.