I remember the Avalon Hill version (not Brief) specifically says you can't.My version of the Avalon Hill version specifically says you can. Pg 3. "9.4. AZTECS & INCAS: These two empires appear on the same card during Epoch VI. They use armies of the same type and if they control two Resource symbols between them, may build a Monument."
Different versions? Or is your answer a typo?
Have yet to play the Brief HotW, but reading the rule book I would say the same applies, because the rules say that your empire does not Resign until after you have played all armies from the Array (pg 9). And that would mean after playing both the Incas and the Aztecs.
Edit: To clarify this, the "reorganising your empire" rule states that
all fleets are removed from the map
all standing armies are resigned
the Empire card is discarded
Because of the third bullet (discarding the empire card) is impossible between playing the Incas and the Aztecs, the Incas will (yet) not have resigned when the Aztecs move. I mean Reorganising simply must happen after both empires have moved.