My reading of the rules would allow the OP's itinerary, though I'd agree that the rules might be somewhat ambiguous.
There appear to be 3 relevant rules here (all in the "Routing" section), 2 of which have exceptions:
Rule 3: 1 INTERCONTINENTAL DEPARTURE AND 1 INTERCONTINENTAL ARRIVAL PERMITTED IN EACH CONTINENT EXCEPT AS FOLLOWS:
- 2 PERMITTED IN ASIA, 1 MUST BE A TRANSIT WITHOUT STOPOVER OR ON DIRECT SINGLE PLANE SERVICE BETWEEN THE SOUTHWEST PACIFIC AND EUROPE.
Rule 4: 1 INTERNATIONAL DEPARTURE AND 1 INTERNATIONAL ARRIVAL FROM/TO THE COUNTRY OF ORIGIN PERMITTED... (no relevant exceptions)
Rule 5: TRAVEL BETWEEN AUSTRALIA AND EUROPE ON A SINGLE FLIGHT NUMBER OR AS A SURFACE SEGMENT IS CONSIDERED TRAVEL THROUGH 3 CONTINENTS SOUTHWEST PACIFIC-ASIA-EUROPE.
Rule 3 seems to clearly allow 2 intercontinental arrivals and departures from Asia, and long as 1 of them is a transit between SWP and Europe. I can find nothing in the rules in which the application of this rule makes any distinction based on continent of origin. However, Rule 4 eliminates the possibility of originating in BKK and then traveling from Australia to Europe via BKK -- the transit point would need to be HKG or SIN.
Rule 5 is where it becomes interesting, as it states that a SYD-(SIN)-LHR trip would be 3 continents. So, does that mean that if you've already been to Asia once, you'd need to count your transit through Asia as another continent (that is, count Asia twice as a continent)? While the wording of the rules might be a bit ambiguous, it seems clear to me that the intent of the Exception to Rule 3 serves 2 purposes: it allows the 2 arrivals/departures from Asia, and it means that Asia is counted only once as a continent, whether or not you take advantage of the exception.
So, my suggestion to the OP is to re-call the AA RTW desk and find an agent who will read the rules more along the lines suggested here.