I'd love to hear suggestions about maximizing mileage on a DONE4 I'm about to book. I live in NYC and the only cities I actually need to go to are Rome, New York, Sydney, Auckland, and Bangkok (well, Ko Samui.) Quick dinners with friends in London and Abu Dhabi will be a bonus, but aren't essential:
CAI-LHR-FCO-(stop)-ORD-(stop)-DFW-ANC-DFW-LAX-JFK-(stop)-SYD-(stop)-AKL-(stop)-HKG-BKK-(stop)-DEL-NRT-LHR-AUH

(Chicago is only in there due to there being no availability to JFK on the date I need to travel. I guess I'll have to buy a ticket from ORD-NYC-ORD?)

A skeleton version of this itinerary is on hold with AA. Any way I can milk some more miles out of it and try to reach the next AAdvantage elite reward tier would be appreciated And is there any truth to the rumor that if the first flight is on BA, then BA's astronomical fuel surcharges apply to the entire itinerary? I'm hoping that's not the case if an AA agent handles the ticketing. If so, I'll have to do some rejigging at the top.