Specifically, I came across Okichitaw which is kind of a modern mesh of Cree musket club combat and Tae Kwan Do.
Are there any attempts to recreate or practice Maya, Aztec, Inca or Olmec combat methods, or a treatise on classic era combat styles, such as Agrippa or Musashi?
We certainly know that all able bodied men and boys among the Aztecs received some measure of military training as part of their universal education system. For the elites this would be part of the intensive schooling on various subjects they received at the calmecac. Commoners would get less extensive education at the neighborhood telpochcalli. Other than that some sort of pedagogy in warfare occurred, however, we have no additional details as to the manner, method, or curriculum.
There's a few reasons for this absence. The first has to do with what you term a "treatise on classic era combat styles." There aren't any. Extant Pre- and Peri-Hispanic contact codices from Mexico are exceedingly rare (FAMSI has scans); they were early and frequent targets of Spanish oppression. Those that do survive (and the Borgia Group are the only collection though to actually pre-date the arrival of the Spanish), do not deal with such "mundane" aspects of life as combat training, but on religious matters and royal genealogies.
The second problem is that we actually have no surviving indigenous arms from that time period, at least none of the specialized weaponry and armor. We certainly have an abundance of obsidian blades which have survived archaeologically, but not a single authentic macuahuitl or tepoztopilli, the last specimens (which were ornamental to begin with) went down in literal flames when the Royal Armory in Madrid burned down in the 1800s. Similarly, we do not have any surviving ichcahuipilli or tlahuiztli armor, and the only remaining examples of chimalli we have are essentially ceremonial artwork, like the gorgeous Ahuizotl Shield. So we don't have much in the way of physical material with which to reconstruct detailed usage, and although we do have numerous depictions of warriors, these are intended to display rank and prestige, not tactics.
Drawing on the Spanish sources is not much help either as they can be equal parts flowery and vague. Here's a typical passage from Díaz del Castillo:
When, therefore, the attack commenced, a real shower of arrows and stones was poured upon us; the whole ground was immediately covered with heaps of lances, whose points were provided with two edges, so very sharp that they pierced through every species of cuirass, and were particularly dangerous to the lower part of the body, which was in no way protected. They fell upon us like the very furies themselves, with the most horrible yells...
The focus, obviously, was not on individual actions, but the state of the battlefield mixed with no small amount of dramatic tension. Descriptions from Cortés are similarly focused more on the big picture. Ross Hassig, in Aztec Warfare, has managed to piece together an account of how the order of battle for Aztec era armies would go, but, again, this is because we have information on the larger picture that we do not have for the more granular training.
So the answer to your question is no, we do not have any artifacts, writings, depictions, or other materials that would allow us to accurately interpret or recreate the training of individual soldier at that time.
For European stuff (like Agrippa, as you mentioned), check out /r/wma. Recreating historical European combat is the raison d'être of that sub, and by extension, the entire HEMA movement.
