Finally got this ticketed (took about ten days from submitting my final itinerary to the credit card being pounded). Had to wait a while so I could get my credit card limit bumped up high enough first.
Final itinerary: ZRH-LHR-ORD-LGA-ORD-DFW-HNL-NAN-BNE-DRW-PER-SYD-NRT-LHR-[PRG-LHR-ZRH]
(We'll save the PRG-LHR-ZRH legs for a weekend holiday later in the year.)
A bit over CHF9100pp (taxes/surcharges/fuel fines inclusive), plus a CHF160 booking fee (which I thought was a bit rude, but in the grand scheme of things is a rounding error).
Now, I can see the itinerary via AA's "My Reservations", and select/reserve seats on the AA flights there, but how do I select seats for the non-AA flights (BA and QF) ? Also, how do I get out QFF #s associated with the flights for the SCs and points to rack up ? Do I need to call up AA's RTW desk again, or is there some way to do it online ?