OK, so I've been thinking about this quite a bit and some of the things people have mentioned is that:
a) long-distance trade would be good to facilitate the exchange of ideas amongst the different cultures that existed in the Americas at the time, but that geography was a problem.
b) Mississippians domesticating more animals would be a good thing; primarily, this part of the discussion has revolved around land animals.
This got me thinking about animals that migrate. Specifically, I was thinking about animals that might migrate from North America to South America. I first thought about Passenger Pigeons and whales, but neither of those really worked - Passenger Pigeons didn't migrate and although whales do, no species I could find seem to go from the Mississippi delta to the north coast of South America.
I found this list of bird migration routes, that mentions a bunch of birds that do migrate from North America to South America:
https://www.birdsandblooms.com/travel/birding-hotspots/where-do-migrating-birds-spend-the-winter/
It wasn't that useful, but confirmed to me there are bird species that do migrate from North America to South America.
I went back to the sea and considered turtles. The Loggerhead Turtle does migrate around the North Atlantic, making stops in Colombia and the Yucatan Peninsula. However, I can't find evidence it stops off near the Mississippi delta:
http://www.arcgis.com/apps/MapJournal/index.html?appid=0eb8545fa3cd4fc38b93efc25b732193
My thinking on turtles is that they might make a good luxury good - their shells being useful, while their meat is edible. Turtles are listed here as "domesticated" but I don't think that's exactly true:
https://en.wikipedia.org/wiki/List_of_domesticated_animals
There are some Native American cultures that believe the world is carried on the back of a turtle:
https://www.atlasobscura.com/articles/world-turtle-cosmic-discworld
It wouldn't be ASB to imagine an intrepid Native American (or a tribe) trying to find the 'source' of the turtles given its place in mythology - each year move a little bit closer in the direction the turtles are coming from. This could also spur sea-faring advances as they attempt this, although maybe that's much more unlikely. It also wouldn't quite bring any Native Americans from Mississippi close enough to, say, the Incas.
Then I remembered that the Mongolians domesticated eagles - or certainly tamed them - and that the relationship between the handler and the eagle is a really close bond:
https://www.newyorker.com/culture/photo-booth/the-eagle-hunters-of-mongolia
And this got me back thinking about birds.
So I Googled "Mississippi birds of prey" and found the Mississippi Kite:
https://www.jstor.org/stable/pdf/24617876.pdf?refreqid=excelsior:a656100a4429e211e1a808957d16b2ff
And look at the Mississippi Kite's migration route:
https://en.wikipedia.org/wiki/Mississippi_kite#/media/File:Ictinia_mississippiensis_map.svg
A quote on their diet: "Their diet consists mostly of insects which they capture in flight. They eat cicada, grasshoppers, and other crop-damaging insects, making them economically important. They have also been known to eat small vertebrates, including birds, amphibians, reptiles, and small mammals." (
https://en.wikipedia.org/wiki/Mississippi_kite)
And on their nesting habitats: "Mississippi kites nest in colonies and both parents (paired up before arriving at the nesting site) incubate the eggs and care for the young. They have one clutch a year which takes 30 to 32 days to hatch. The young birds leave the nest another 30 to 35 days after hatching. Only about half of kites successfully raise their young. Clutches fall victim to storms and predators such as raccoons and great horned owls. Because of the reduced amount of predators in urban areas, Mississippi kites produce more offspring in urban areas than rural areas." (
https://en.wikipedia.org/wiki/Mississippi_kite)
So imagine that the Native Americans domesticate the Mississippi Kite, using it to help keep their fields free of pests. The Native American handlers form bonds with the birds like the Mongolian Eagle handlers did/do with their birds.
Whilst I was researching migrating North American animals, I also found this passage about bison: "The first thoroughfares of North America, except for the time-obliterated paths of mastodon or muskox and the routes of the mound builders, were the traces made by bison and deer in seasonal migration and between feeding grounds and salt licks. Many of these routes, hammered by countless hoofs instinctively following watersheds and the crests of ridges in avoidance of lower places' summer muck and winter snowdrifts, were followed by the aboriginal North Americans as courses to hunting grounds and as warriors' paths. They were invaluable to explorers and were adopted by pioneers.
Bison traces were characteristically north and south, but several key east-west trails were used later as railways. Some of these include the Cumberland Gap through the Blue Ridge Mountains to upper Kentucky. A heavily used trace crossed the Ohio River at the Falls of the Ohio and ran west, crossing the Wabash River near Vincennes, Indiana. In Senator Thomas Hart Benton's phrase saluting these sagacious path-makers, the bison paved the way for the railroads to the Pacific." (
https://en.wikipedia.org/wiki/American_bison)
Given all this information, I tentatively propose the following: An early domestication of the Mississippi Kite, used for keeping fields free of pests, prompts changes in Native American belief systems. A 'Holy Trinity' of animals become sacred to the people of the Mississippi; the bison is the God of Land and Warriors, the Mississippi Kite is the God of the Sky and Hunters, and the Turtle is the God of the Sea and Priests. Belief in these gods means that the Native Americans start becoming interested in tracking their migrations. Eventually attempting to follow the migration of your chosen 'god' becomes the Native American version of a pilgrimage or Hajj. The Bison Pilgrimage is the first that is 'perfected', the Mississippi Kite Pilgrimage is the second to be 'perfected,' and the Turtle is considered impossible but spurs seafaring innovation as followers of the Turtle God of the Sea and Priests attempt their pilgrimage.
Now, the best thing about this is that birds don't tend to migrate over water. They avoid it. So when the Mississippi Kite does migrate to South America, it goes via Mexico, Panama, and the Andes. This would take any pilgrimaging Native Americans right past the tin at Zacatecas:
https://www.google.com/maps/search/Zacatecas+tin/@23.0677013,-104.7920505,7z
Some of this might seem unlikely, but cultures all over the world have decided animals are holy (cats in Ancient Egypt, cows in India, Hedgehogs in Sikhism, etc) and we know people will do anything for religion - except the Ancient Greeks who wouldn't even walk up Mount Olympus to check if their gods were actually there.
We also know people are willing to follow animals that are important to them to the ends of the Earth:
https://en.wikipedia.org/wiki/Evens
And we know that walking from North America to South America is possible:
https://matadornetwork.com/read/meet-first-man-walk-14000-miles-argentina-alaska/
So that's my idea for a TL developing.
You can call it, "The Kite, the Bison, and the Turtle."
Northstar
P.S. I know the Inca didn't yet exist in the timeframe we're talking about, but you can still get an exchange between North America and South America going with the pilgrimage I talked about, thus when/if the Incas do develop you already have an existing system in place that can facilitate the exchange of animals/culture/innovation.