The Starfiles for different fare types contain all the applicable rules. (Someone more knowledgeable than I should be able to give the pukka definition.) Copies of these float around the web & FT, but clearly only the most up-to-date applies, and the most recent that I can find for a DGLOB34 is from 2005! However, a definitive resource is the AA RTW desk in the US and the copy Starfiles I have seen start:

** UNIVERSAL STAR **
U STAR ID - GLOBAL EXPLORER
0S GLOBAL EXPLORER
1N .
2N . ** FOR INFORMATION ON THIS FARE PLEASE CALL THE
3N . AROUND THE WORLD DESK AT 1-800-247-3247 **
4N .

My view is that you should get on to the AA RTW desk ASAP. They should be able to set it all up for you, get it priced (in Dublin, I believe) & give you a reference with which to contact AA Switzerland to issue the tickets. They should also be able to confirm the QF/FJ reservations (if the D inventory is still there). If they can't make the reservations, they should advise you how to proceed. This should enable you to take the trip via Fiji as you'd planned.

Received wisdom seems to be to (politely) clear the call & try for a different agent if the first agent is poor. (DGLOB34s are not that common, so don't expect someone to know all the rules instantly.)

As for the rather limited OneWorld offering via HNL, I'm inclined to agree. I have an AONE5 coming up & avoided a HNL routing because of the lack of First cabins from Oz.