With a *A bias things are tough, but unless you're willing to defect to OW / QF, I guess I would be leaning on SQ or NZ. With the latter you can go PER-AKL-SFO-IAH which is probably the most direct routing -- I don't know of a way to do this city pair with only one plane change -- and avoid LAX in the bargain. Last segment on CO or UA.

With SIN it's PER-SIN-(NRT)(HKG)-(SFO)(LAX)-IAH. A little longer trip, a little better service.