Thanks to everyone for their thoughful replies. As mentioned in a different post, I can take the Qantas flight SYD-LAX-JFK which has a single flight number, so it won't count as my North American transcon. I could then do JFK-SFO-ORD-JFK (3 segments, one transcon) and LGA-ORD-SFO-ORD(3 segments) and find a way back to NYC from there.

I'm trying to convince my wife now, and my best argument seems to be the opportunity to visit places that are out of the way and normally have expensive fares. Instead of maximizing miles I would prefer to travel to more costly locales, like the Canary Islands, Cairo, and Easter Island. Where else are "high-ticket" destinations that you could get to on a OWE ticket?