It'd be great to be able to extend or shorten our stay in a given city without having to pay hefty fines. If that's how RTW tickets work, I'd be happy as a clam but from the routing applications that I've been using, you need to pick the dates.
Oneworld RTW tickets do exactly that. If the ticket is electronic (which they usually are) you have to pick dates because you can't have open-dated segments on an electronic ticket. However, provided you don't change the routing, changes to the date/time/Oneworld carrier are free. Routing changes are $125 every time you make a change. The only thing to watch out for if you're going to be changing dates as you go is whether there is inventory available when you need it. Oneworld economy RTW tickets book into "L", which is a relatively low fare class, so not always available when you need it.
I just found a one way fare sale to get us from LAX-SYD for 525 per person which seemed like it was a lot cheaper than anything else I'd seen. I need to figure out if it makes more sense to just buy a multi trip ticket or one way tickets using sales etc if it would be less expensive.
Which airline? If this is a Qantas 'deal' (given your preference to stick with Oneworld), that fare probably has to be on a roundtrip basis (and probably has to be roundtrip on just about any airline to be that price) and probably won't earn any AA miles. Caveat emptor.
[Edited to add]
Wow - I guess Air New Zealand is desperate for business - $390 + $45.20 in taxes = $435.20 one way for LAX-SYD the week of April 5 ....
As that goes via Auckland, could you make that (NZ) your first country and then on to Oz from there?
Note also that RTW tickets in economy are cheaper if you start in Australia (or NZ) than the US - you would have to end up back in Australia (or NZ) if you start the ticket there but that can always be 12 months down the road (and of course you may just 'forget' to take that final flight...).