I just flew SFO-SIN and am returning Tuesday. After getting the flights I called AA and they booked it all in H, codeshare plus the CX segs, in a roundabout itinerary.

Warning though. Availability is tight. I had to rebook my return and to stick within the $100 change fee it had to be in H and there was almost no H availablity for days. Price difference was an extra grand. But thanks to Expert Flyer I found one return flight with H2 and booked it, via JFK but saved a lot.