Well, if you join (or are already part of) Krisflyer, you get double miles on SQ 19-20 through June, to recollection. Doesn't help your UA status, but gives the same number of Star-usable miles.

Basically, the 345 is quantum leap in long distance airplane travel. Seat comfort, space between seats, IFE and the convenience of a nonstop are well well beyond UA, even in E+. I slept about 7 hours each way, which simply doesn;t happen in eeconomy (for me). The other SQ flighte are nice enough, but the only major upside is the IFE (which certainly helps)

Now if you can upgrade the UA ticket somehow . . .