The LAX-SIN direct flight is all business class at the end of Sep, no more executive economy. I believe weight savings and profit are the reasons they went this route.
There are flights via TPE from LAX. I haven't flown that route since last year when I had a stopover in TPE. Not a fan of that airport even for transfers.
The direct flight is from EWR-SIN. A buddy of mine became a Virgin convert after he flew from IAD-LHR-SIN. The IAD-LHR was a code share with Virgin and Upper Class plus the Virgin lounge in LHR made him a convert. The LHR-SIN was a SQ plane. If you are carrying a lot of hand luggage, LHR is known to be pretty draconian about cabin luggage nowadays. Even my dad, who loves London, hates LHR now since they made him check his 2nd piece of luggage earlier this year.
Eva airline still has Economy Plus service betw LAX and SIN.
If you want to use your miles to upgrade the SQ tix... be quick! They have limited the seats even more now.