Regarding the Mexica defeat at the hands of the Europeans, I am an adherent of Diamond's Guns, Germs, and Steel argument. Disease played a hand, as well as the Spanish advantages in the horse and the profound tactical advantages it conveyed over an opponent unused to dealing with cavalry.
Indeed, the Spanish of the period were the elite soldiers of Europe, were imbued with a degree of supreme self-confidence that only such devastatingly successful combat veterans can possess, akin to the elite combat units of the 20th century such as the US Marines during WW2, the Legion Etranger, or the SAS. hence their willingness to wade into many times their number of native warriors and slaughter them in droves.
The advantages conveyed by the horse cannot be underestimated, however had the Mexica and other indigenous peoples been able to adapt their tactics to the new threat presented by cavalry -ie., employing longer spears or pikes in tight, disciplined formations- they may have been able to at least force the Spanish into a stalemate in the short term, and made the conquest of the Americas all the more difficult and prolonged. This was the single great tactical disconnect, a (local) style of warfare designed for 100% infantry armies optimized for flexibility in battlefield deployment and maneuver and adapted to the lack of a domesticated beast of burden able to carry supplies and/or men over protracted distances, squaring off against some of the very finest metal-clad shock cavalry Europe produced during this period of history, an opponent/weapons system with which the Mexica had absolutely no conception of prior to their arrival, and the Spanish were shrewd enough to not give the locals any breathing space to figure out the logical solution (ie., pikes).
The Aztecs/Mexica did not lack unit cohesion or discipline; their formations and maneuvers were perfectly suited to their environment and style of fighting. Units could rotate ranks in a disciplined fashion reminiscent of the Roman Legions, do so efficiently and without compromising the cohesion of the overall battle line against their own, local opponents who fought in much the same way. What they lacked was a style of warfare designed to resist shock cavalry. The various civilizations that had the benefits of first chariots and later cavalry employed for shock action soon enough learned that in order for infantry to survive a confrontation with charging cavalry, they had to stand in close order, with spearpoints or better still pikes leveled enmasse and steady. When this formula was employed, shock cavalry found it damn near impossible to break such an infantry formation.
The Mexica as you pointed out had no prior experience with an animal anywhere near as large as the horse, so they had no baseline for sorting out the advantages and disadvantages of cavalry until it was far too late.
Now all that aside, I submitted this proposal with an eye towards Pre-Columbian warfare, not necessarily towards La Conquista period "turkey shoots." Against their own the Mexica were formidable opponents, and an Aztec army deployed on the tabletop is a riot of color and pageantry, and can double as a very handy fantasy human army as well.