As I am fairly interested in New World timelines and the OP's question, I figure I'd go a bit more into depth with what I see as
possibilities. Mostly I'm taking all the current New World Domesticates TL's and mashing them all together. There are two ways to go about a "best case" scenario. Save megafauna, or don't and work with what's left. If you do the former you get all sorts of things like horses, camels, Llama, and possible exotic things like Mastodons. But you kind of ruin any possibility of OTL cultures developing, so I'll outline a possibility without that.
The earliest things that have been explored are the PoD's involved in Pecari Rex, Land of Salmon and Totems, and Mississippi Rice. All three involve genetic changes to make three things more amiable to domestication (albeit, later versions of Pecari Rex saved the horse, so we won't do that) several thousand years ago.
Technically, these too are so far back that everything would be different, but it's a minor thing I think, we can ignore that for the sake of story, right?
After that, Lands of Ice and Mice involve a PoD too late, 717, though the actual PoD is a cultural shift in the Thule Culture, brought on by a fluke. No real reason as far as I can see why you can't roll this down to something earlier, perhaps 200AD. Late, but before the cut-off point. There was some talk about the PoD being around the Medieval Warming period, but I don't see this as necessary for a change, just helpful. If everything went along as in Ice and Mice, just five hundred years earlier, that's a decent chunk of time.
The other two timelines that come to mind are Bronze Age New World, and Guns of the Tawantinsuyu. Then preventing the Pre-classical Mayan collapse has been suggested, as well as fish farming.
With moderate uses of butterfly nets, you can keep most South American cultures the same, or at least known. The Maya and Olmec will probably exist in a fairly recognisable way, only this time there are Pecaries just waiting to be domesticated. Assume a bigger population, and assume either no pre-classical collapse, or a less devastating one. The former is better for our purposes.
The far north hasn't diverged yet and the rest of North America is starting up in a similar fashion, Mississippi Rice positing a Megalopotamian Agricultural Complex developing at
around the same time the Olmec would be showing up, and Salmon and Totems also positing the introduction of a Willamette Valley civilization with their River Potato. The Megalopotamian agricultural package has an awful lot of things, the rice being only the most important, while the Willamette Valley package is much smaller. The area also has fish farming, so there's that. There are also mentioned domesticates, and of course we should
assume domesticates in different areas. American Bison, Turkeys, Heath Hens, Muscovy Ducks, Peccaries, Blue-winged Teal, Mallards, Mountain Goats, and the OTL stuff like guinea pigs, dogs, and Llamas. All these combined give North America everything the old world had, except a Horse analogue. This is the only reason I'd perhaps accept the survival of the horse. It'd be really helpful here.
The Andean area would develop on its own, alone, for a while, and it will still be first. We can put a net over it so it trucks along until 1200BC or so. The Pecaries are here too, so things will change also from that.
By 200AD, everything has changed. All of the Americas have some major useful agricultural package, and has seen the rise and fall of empires, except for the Far North which is just getting on its feet with an earlier Ice and Mice. Whatever alternate-Saladoid culture arises in the Caribbean will have come from a more populous, stable central America and south America. Whatever the case, you can assume a maritime culture, an alternate "Polynesian Arawak" culture in the Caribbean. This can now greatly increase contact between Mesoamerica and whatever has developed in North America. Guns of the Tawantinsuyu assumed an accidental discovery of Gunpowder in 800AD, but no reason you can't now bump that down to around now in the Andes.
Contact is 1492. So now we have nearly 1300 more years to develop before then, and all the pieces are there to move to Bronze Age, to Iron Age quickly, (there is a suggestion that some Iron-working was spurred forward due to a decrease in the availability in bronze, but bronze would be hard to come by outside of Mesoamerica and so an Iron-age could be pushed forward thanks to that)
From an iron age, it's just a hop-skip-and-a-jump to something recognisably "even" with the Old World, so long as everything was pushed that way.
People suggested longer Viking Contact. This would start in 900AD, which would have given our intrepid Thule 700 years to learn the ropes of agriculture, which is significantly longer than they had in Lands of Ice and Mice. You could probably get "European knowledge" to trickle into the new world much easier in this scenario, maybe European things like chickens, but it would make it harder to keep a butterfly net around the Old World. You'd also probably get heavier die-offs from disease, but probably still not much spread of immunities.
Do all this and you have everybody's suggestions and previous ideas all at once, and without ASB's the new world in 1492 I expect could be fairly "even" with the old.
Back to disease, the New World would have developed its own crop of diseases, which I think will save it. People talk about how you can't get the New World to not experience huge die-offs. True, but if they have their own diseases, any would-be early explorers like Columbus will stay long enough to get sick and die. If there did manage to be enough survivors to take a ship back to the Old World, and as contact increases, the New World will probably introduce some nasty plagues, putting the Old World in the same boat as the New World. Europe will recover. So will the New World. And because it's two-way, Europe can't just walk in an take advantage of New World instability from diseases. Europe has its own diseases to worry about now.
I never said that there is absolutely no possibility that lllamas could be moved north.
My mistake, I was confused by the bolding of the word "won't" and the assertion that it was a "non-starter." I should have known you actually meant the opposite of what you said.
What do you think you were saying then? It couldn't have been just pointing out that things won't move if people don't want them to, considering you already said that and I already said that, and nobody contests that. It couldn't have been asking
how, because you said that after I'd already explained that it's not quite a good time to go into the "how" just yet and we were already
assuming trade was happening with certain desires and tech levels. So what was it then? What were you saying, if not that it was impossible?