CX has had the midnight and 2am departures from LAX for a long time. They have added the midday departure just this July, going to daily service today, August 1. I have taken both the midnight departure, and the 1pm departure. I strongly prefer the 1pm departure. I am awake and able to enjoy the meal and the service, then get a good sleep, awake and eat some more. When I take the midnight departure, all I want to do is sleep.

Another advantage of the 1pm departure is that it lands in HKG at 7pm, whereas the midnight flight lands at 5-ish am. I can stay up a few hours, then go to bed on HKG time. I clicked right into local time when I took the 1pm departure, whereas that doesn't happen for me when I arrive at 5am. Your arrival times will be +5 hours or so in SIN, but the concept is the same.

I would maximize the pleasure of the long haul flight, and let the onward flight to SIN fall wherever.