Good grief, the TA's ticketing dept insisted that they're correct and that they've used AA's "template" to charge tax/fuel fines.

AA's tax/fuel = A$473.75 (which already includes A$218.65 of YQ)
TA's tax/fuel = A$647 (excluding service charge)

AA's amount also tallied with what was worked out by a TA on another travel forum.

Any idea how I could convince the TA to reconcile the figures with AA?

Unfortunately I can't cancel the itin and book with AA due to reasons cited above and also availability has gone down to L0 on some of the crucial segments.