I actually think your original routing looks fine, so not sure where the snag is. If you had dates (or sample dates where it did not work) would be helpful. I'm guessing married segment issues but those can be broken sometimes on the OneWorld stie. AA will stick to the rules (and know them as well), so anything that should be input as a married segment will be, however the OneWorld site gives you some leeway on that.

Other benefit of non AA ticketing is that if you are after AAdvantage miles, you can book AA segments as codeshare flight numbers on partner ticket stock but not on AA ticket stock. Makes a big difference if you can book AA flights as BA, IB, or QR flight numbers, for that matter even if on QF or JL numbers you'd still be better off, not sure they codeshare with CX or MH these days .