I liked the idea of the Chinese reaching the Americas before Columbus would have in OTL, and came up with a possible story for how they could have done so in an ATL in which European civilization is virtually wiped out.
The Silk Road was the previous connection between East and West, but with European gone, the West is not supplying or demanding many goods, drying up trade along that route. I'm assuming that even if there are few people left in Europe, the unclaimed land and natural resources in Europe would be desirable for other civilizations. With the Timurids and Turks in the way, the Chinese might see that there is too much land-based competition in their way (and too much distance) to gain direct access to Europe's land and resources. So perhaps an adventurous Zheng He analogue (since the POD is ~1350, Zheng He, born in 1371, is butterflied away) decides to find an overseas route to Europe across the Eastern (a.k.a. Pacific) Ocean in the early 1400s. (AFAIK, the Chinese were not under the misconception that the world was flat, unlike the many Europeans who in OTL doubted Columbus's belief in a round Earth.) Conceivably, to the Chinese, it could be a quicker route than rounding Africa.
Of course, the Chinese expedition does not make it to Europe. Instead, they stumble across Hawaii, and, encouraged by this discovery, they continue on to the Americas, maybe landing in Mexico. Here they encounter the Aztecs and begin to trade with them, with Aztec gold and chocolate being some of the favorite Chinese imports. The length of the journey is somewhat daunting, but their new Hawaiian colony serves as a useful stopover. However, the increasingly isolationist attitude in China results in more limited trade and prevents extensive colonization of the Americas, but trade is not cut off altogether. (I'm not certain why the Chinese would be any more benevolent toward the native Americans than the Western explorers in OTL.)
Old World diseases such as smallpox and measles have their way with the Aztecs and spread throughout the Americas, but in the absence of conquistadors, the native Americans are able to recover without being overrun by Old Worlders. I don't know how long it would take them to evolve resistance to these diseases, nor do I know how they would handle the bubonic plague. In OTL, the plague for some reason did not reach the Americas until the late 19th century, so perhaps its arrival could be similarly delayed in the ATL. With the continual low-level contact with the Chinese, the native Americans could acquire Old World metalworking knowledge and technology, as well as domestic animals and crops (which are both good and bad for the Americas). Perhaps an ambitious, forward-thinking Aztec leader helps to acceleration the adoption and adaptation of Old World tech, giving the native Americans a better chance to ward off future invaders from across the Atlantic.
In the West, Europe has been fought over primarily by the Ottoman Turks and Mamluk Arabs, with the remnants of former European governments ground underfoot in the process. Eventually, the Turks and Arabs begin to extensively explore overseas, although much later than the Europeans in OTL. (Maybe they reach the Americas in the 1700s or 1800s? What time is reasonable? The more time the New World has apart from the western Old World, the better, but I can't delay contact for an unreasonable amount of time.) If the native Americans are given a few centuries of lead time, maybe the Old Worlders establish much smaller colonies in the Americas but cannot colonize too far inland due to native American resistance. Thus, the Aztecs retain control over Mexico, Central America, and the Caribbean, and the Incas hold onto the western half of South America. And maybe even some tribes of native North Americans form an Aztec-supported coalition which reigns over what in OTL is the central United States.
Does this all sound plausible? Any input is welcome. I think the most crucial (and potentially weakest) parts of the premise are (1) how well the native Americans can develop resistance to Old World diseases; (2) how well they can adopt and adapt Old World technology; and (3) how long after contact with the New World by the Chinese in the early 1400s will contact by the western Old World occur.
Also, Locke, please let me know if this is too close to what you had planned for your timeline. I really don't want to step on anyone's toes or replicate someone else's timeline.