I'd encourage you, for the 5K miles, to consider the QR-JL routing. I've done JL in F in both directions from LAX and can say it's one of my better travel experiences. I certainly think it's superior to CX, notwithstanding the slightly less private seat. Better service. WAY better food and drink. And although NRT might lack some of the ground amenities in the lounges, the transfer experience is for me just a little easier and more manageable. I quite like the JL F lounge, too. It's not over-the-top, but it's nice.
One option for you consider that's a little more direct, if you can find the space: MLE-CMB-NRT. CMB-NRT is served by UL. I'm pretty certain that is a year-round route, and current schedule shows it operates Su, W, Fr, Sa. I can't say UL's A330 business service is amazing (it's mediocre actually), but the more direct routing might make a difference for you. And the seat is certainly OK for sleeping.
In NRT you can exit the airport and take the short train ride into Narita town, a cute area to have a lunch and spend a little time walking around before heading back to the airport. Go back and shower in the lounge prior to your flight, and enjoy ample supplies of fresh sushi!