Chinese and Korean myths aren't really "goddish". They worshipped ancient kings, or had a religion, like Buddhism, Taoism, etc.
Japanese might be a bit better off than those two, but they still wouldn't fit too well.
India won't work, since Hinduism is still worshipped today.
The thing that I think will fit best into AOM is mesos. But they have their problems too, for they don't have many mythological units(instead, they've got tons of gods). I'll try to present a thingamajiggy on what I think the mesos should look like:
The AztecsMain GodsHuitzilopochtliThe Aztec god of war and of the sun, chief god of the great Aztec city Tenochtitlan. He is a son of Coatlicue. He slew his sister Coyolxauhqui and tossed her head into the sky where it became the moon.
Huitzilopochtli was represented as a hummingbird, or with the feathers of a hummingbird on his head and his left leg, with a black face and holding a snake, and a mirror. His name means "Hummingbird of the South", "He of the South", or "Hummingbird on the Left". Quetzalcoatl"Feathered Snake". One of the major deities of the Aztec, Toltecs, and other Middle American peoples. He is the creator sky-god and wise legislator. He organized the original cosmos and participated in the creation and destruction of various world periods. Quetzalcoatl ruled the fifth world cycle and created the humans of that cycle. The story goes that he descended to Mictlan, the underworld, and gathered the bones of the human beings of the previous epochs. Upon his return, he sprinkled his own blood upon these bones and fashioned thus the humans of the new era. He is also a god of the wind (the wind-god Ehecatl is one of his forms), as well as a water-god and fertility-god.
He is regarded as a son of the virgin goddess Coatlicue and as the twin brother of Xolotl. As the bringer of culture he introduced agriculture (maize) and the calendar and is the patron of the arts and the crafts. In one myth the god allowed himself to be seduced by Tezcatlipoca, but threw himself on a funeral pyre out of remorse. After his death his heart became the morning-star, and is as such identified with the god Tlahuizcalpantecuhtli. In dualistic Toltec religion, the opposing deity, Tezcatlipoca ("Smoking Mirror"), a god of the night, had reputedly driven Quetzalcoatl into exile. According to yet another tradition he left on a raft of snakes over the sea. In any case, Quetzalcoatl, described as light-skinned and bearded, would return in a certain year. Thus, when the Spanish conqueror Hernán Cortés appeared in 1519, the Aztec king, Montezuma II, was easily convinced that Cortés was in fact the returning god.
The Aztec later made him a symbol of death and resurrection and a patron of priests. The higher priests were called Quetzalcoatl too. The god has a great affinity with the priest-king Topiltzin Ce Acatl Quetzalcoatl, who ruled the Toltecs in Tula in the 10th century. The cult of Quetzalcoatl was widespread in Teotihuacan (ca. 50km northeast of Mexico City), Tula (or Tullán, capitol of the Toltecs in middle Mexico), Xochilco, Cholula, Tenochtitlan (the current Mexico City), and Chichen Itza.
TezcatlipocaTezcatlipoca was the Aztec god of night and all material things. He carried a magic mirror that gave off smoke and killed enemies, and so he was called "god of smoking mirror." He was god of the north. As lord of the world and the natural forces, he was the opponent of the spiritual Quetzalcoatl, and sometimes appeared as a tempter, urging men to evil. Punishing evil and rewarding goodness, he tested men’s minds with temptations, rather than trying to lead them into wickedness. He was also god of beauty and war, the lord of heroes and lovely girls. He once seduced the goddess of flowers, Xochiquetzal, wife of the god Xochipilli, because such a lovely goddess was a good match for him, being a handsome war-like god. Yet he appeared most frequently as a magician, a shape shifter and a god of mysterious powers. Favor Gathering SystemAt their temple, they have 2 ways to gather favor. They can 'sacrifice' food/wood/gold to the temple, in order to get some favor. This would work much like the way the market works, except at a high currency of around 5 favor for 100 food/gold/wood. This means that 2000 food/wood/gold will get you 100 favor.
Another way is the human sacrifice. They can order their units to go to a temple(like garrisonning). Then, that unit 'dies' while you get some favor. A villager might give 5 favor(while this may seem expensive, remember that a villager only costs 50 food. This is half the price of sacrficing resources). Each military unit would give different amount of favor, depending on its cost. You will not be able to sacrifice siege weapons and mythological units.
Special PropertiesThe Aztecs start with 5 villagers, but instead, no scout. However, they can buy a weak scout for some food. The Aztecs don't need to deposit their resources. What I mean by that is, they just keep gathering without needing to deposit their resources, unlike other civs. To compensate for this, their gathering speed is a little slower.