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"I can book--right now--the dates we want next summer on Qatar in business class from LAX-CPT-JNB-SFO. The connecting flights from SFO to LAX don't open up for another two weeks."

You can't book award flights on any carrier more than 331 days in advance when redeeming AA miles, even if the partner carrier makes award seats available to its members (or its other partners) more than 331 days before departure. And it's really impossible to know when (or even whether) AA will make SAAver seats available on the SFO-LAX (or the SJC-LAX) route. What dates are you looking at for outbound and return travel?

Since all AA awards are offered as one-ways, you could redeem AA miles for the outbound to CPT; BA Avios (or cash) for CPT-JNB; and maybe even Alaska Airlines miles for JNB-HKG-SFO (62.5K Alaska miles per person in J, with a free stopover in HKG, if desired). SPG transfers to AS; and there are also AS-earning credit cards with sign-up bonuses. If you'd rather save your SPG points for something else, JNB-HKG-SFO on CX in J can also be had for 85K AA miles, with a free stopover in HKG, since you would be redeeming for two separate AA awards per person.

Of course, finding two J award seats on the same flights can be challenging regardless of which carrier you fly.