Inka last for longer, but...
I'd considered writing a timeline on the Inka along somewhat different premises, my research so far netted the following.
At the time of the Spanish conquest the Inka were looking at expansion into the Silver River basin (OTL northern Argentina, Paraguay, and Uruguay), central and western Colombia, eastern Peru/western Brazil via the Amazon River, and the southernmost reaches of Chile below the Bio-Bio river. With an extra two centuries you just avoided the Inka civil war - Spain may not be able to take the Empire on that basis alone. Inka metalsmiths were working copper in addition to gold and had a trade route with the Aztecs among others via Jalisco, they would receive word about the pale-faced demons looting the gold and killing the people. With any sort of preparation they will be a formidable force, even with 90% population reduction the Inka of OTL would number approximately 1.5 - 2 million people, certainly enough for a functional state, and with population expansion over two centuries perhaps 4 million or more after said reduction. Inka technology had certain areas of advantage as well, their road system was extraordinary as was their ability to make textiles (1000 stich/in^2 would not be seen again until the 19th century of so). They also had hematite, known to the Andes as a pigment since 100 AD or so, thus it would be possible for them to eventually produce steel under the right circumstances.
Given two centuries head start, I think the Inka would expand in almost all directions with rivers and accessible valleys, perhaps even reaching the Atlantic in Uruguay/Argentina/Brazil and at least Manaus/Lugar de Rio Negro in the Amazon. The Musica of central Colombia will probably come under Inka control and perhaps Lake Maracaibo or Darien will see an Inka settlement. Trade with locals in those areas will eventually spread parts of Inka culture and may give rise to satellite states or proto-Inka satellites. The road system will expand accordingly with river trade routes providing supplementation. Cities deep in the jungle (which have been noted as about a dozen from one civilization in Brazil, each as large as 25,000, by archeologists recently not counting whatever they found on the Peruvian-Brazilian border a few years ago). would be able to avoid Spanish or other European notice fairly easily. And with superior numbers the Inka would be able to launch counterattacks and destroy or take over isolated settlements. Steel would be among their most valuable commodities, horses would become a status symbol and food source.
Overall I see three possible scenarios:
1. Inka last a few decades longer with more ruins intact as the Spaniards do not return until the 1560s or 1570s after the plagues decimate the population. A wave of apocalyptic warfare ensues among the Inka and weakens them internally, allowing Cuzco and the mountainous areas to fall with gold production beginning about half a century later than OTL. The Amazon areas are less developed and devolve into city-states as Potosi remains important for the mercury since that was necessary to refine the gold ore - only two locations in the world were known to have it in the 16th century, the other was in Austria. Phillip II will grow his empire accordingly and Europe might be speaking a lot more Spanish by 1640. An isolated city or few cities may hold out well into the 18th century by escaping notice and staying out of sight, if they hold out long enough they might be able to make their own terms about joining one of the new governments or even make a play for independence themselves.
2. As above but the Amazon infrastructure is more developed and the Inka slowly begin to rebuild their numbers. Lost explorers are interrogated at length, the mountains slowly see more Inka influence, and a cult grows among the Inka for their eventual return. Slowly the Inka retake frontier settlements before launching an all-out assault and retaking Cuzco at some point in the early-mid 1600s. Spanish control of Peru, Bolivia, Chile, and Ecuador is lost but they retain Paraguay, easternmost Bolivia, Argentina, Uruguay, Colombia, and Central America does not end. Eventually an uneasy peace is made after Inka governors realize that the Spanish will keep coming and that these 'Yoo-rou-peh-ohns' can be played off of one another. Embassies are sent to England, France, Netherlands, Portugal, and Austria with mixed success. Eventually the Inka come into their own but never as a first rate power, they slowly industrialize and survive into the modern day as a native state somewhat better off than their OTL counterparts.
3. A devastated Inka Empire reorganizes and repels the Spanish. They begin to take back parts those frontier settlements of their empire lost to the Spanish after repopulating for a generation or two. Only later are Englishmen and Dutch traders allowed in but they trade gold for technology, eventually permitting an Inka Empire controlling most of South America and parts of Central America to emerge over time. Southern Chile remains an independent Mapuche state but large parts of Patagonia remain undeveloped for many years, eventually Europeans settle here as they will in eastern Brazil. Central and Southern Argentina become a sort of South American version of Texas but stay within the Empire as a self-governing province with major internal autonomy but no foreign relations of their own and a common currency (think a big version of Hong Kong of OTL). The Silver River valley and everything within 100 miles or so of the river itself remains Inka though. Ironically stevia, native to Paraguay, becomes a major trade item much earlier than OTL. Standard of living is higher and the Inka are a second-tier power by all standards with tourists marveling at intact and well-preserved stone cities.
