A little thinking out loud before I get back to work. I'm not good with map functions, so I'll leave it to someone else to actually put up any kind of map showing stuff. But here's what I've got....
http://www.daftlogic.com/projects-google-maps-distance-calculator.htm
You can use this handy distance calculator to figure out relative distances. Let's assume that Macaronesia is fully discovered and is an important producer of Mastic and Coffee as specialized luxury commodity, with substantive shipping from there to the med, and perhaps between the islands.
The Canaries are probably the center of the trade. The closest island is 62 miles from the mainland. The most remote is about 290. Between the islands, the distances vary from 30 to 70 miles. So you've got some modest deep water hopping about.
The Madeiras are about 300 miles from the Canaries, sailing north. And about 400 miles from the coast. So literally, as the crow flies, they're as easy to reach from the Canaries as from the coast. Or perhaps the other way around. If you look at the prevailing winds, we seem to be in the Northeast Trade winds, which would mean that the winds blow readily from the Madeiras to the Canaries. So most likely, you'd see the smaller Madeiras production being a satellite to the Canaries. Madeiras ships would take the sea route to the Canaries and then from there get to the coast and make their way north. The Madeiras and Canaries would almost certainly form an economic unit, and there'd be at least a couple of reasonable deep water voyages.
Now the Cape Verdes, farthest to the South. They're about 400 miles off the African coast at the closest. The islands stretch across 200 miles, which is a pretty decent 'catchers mitt' What I mean by that is someone sailing deep water south would have a 200 mile wide opportunity to come to the 'findable vicinity' of the Islands - by findable, I mean things like being able to spot from a crows nest, or noticing the seabirds flocking around the area, stuff like that.
It's an 800 mile run as the crow flies from the Canaries to the Cape Verde, and the Northeast Trade Winds are going in the right direction. The African coast is to the East. It looks like you could depart that coast heading for the Cape Verde's at any time. The most likely jumping point is the lower shores of Western Sahara or the northern shores of Mauretania. That would be 500 miles give or take of open water, but you'd have the winds at your back. Any further south, and the trade winds would be taking you south of the Cape Verdes, you'd have to fight them to get back.
The most likely trade route for the Cape Verdes would be to take the Southeast Trade winds from the Canaries or Northern African shores in, then struggle your way back to the African coast and crawl north along the shores.... which would take you right past the Canaries. So again, the Canaries would probably be the dominant part of an economic unit.
Assuming that there's an African production, and assuming its centered around Liberia, and assume you hug the coast... that's a 1700 mile coastal voyage from the vicinity of the Canaries. Or a 2500 mile trip from Gibralter. South of the Canaries is a 900 mile stretch of coast that's the Sahara and Sahel, pretty barren and inhospitable. So the Canaries are likely the most sensible re-provisioning and transshipment point. Again, the Canarians are going to be holding the bottleneck for any African trade.
The prospective distances for an African trade are pretty daunting. If you look at the trade winds...
http://kids.britannica.com/comptons/art/print?id=166714&articleTypeId=0
All the trade winds, the Northeast Trades, the Southeast Trades are going in the wrong directions, and you have the Doldrums to contend with. There's no real choice but to go coast hugging, which also means that you're stuck with a slower voyage and more effort to get there. It's safer, I suppose, blue water sailing is risky. But that's a very limited trade off. Anyone who wants to try a blue water short cut in this area... they're dead men.
Looking at this, I'd say that the economics of an African trade are going to be pretty marginal and entirely under the control of the Canaries.
Now, the Azores make a kind of interesting situation. They stretch across 380 miles, although most of the Islands are found within 240 miles of each other. Their closest point to Europe is the Portugese coast, almost 900 miles as the crow flies. Roughly similar from the African coast. But they're only about 540 miles from the Madeiras. And they're about 700 miles from the nearest Canary islands.
Given these distances, I'd venture to say that they're part of the economic/trade/travel network for which the Canary Islands are the metropolis. The Azores would be in an interesting position though.
As far as winds and currents, take a look at this....
Interesting article right here...
http://en.wikipedia.org/wiki/Volta_do_mar
The Azores aren't quite in the Northeast Trade wind which blows south and westerly. Rather, they're in the Horse Lattitudes or the Westerlies, which blows towards Europe. Although there's an interesting thing - if you look at the maps of winds, it looks like the Azores are subject to different wind directions at different seasons. In July, it seems that the winds are moving from Azores to the Canaries, in January, the winds are almost opposite, and your sailing would be from the Canaries to the Azores. This suggests a seasonality to the Canary/Azores economic interactions.
From these depictions, my guess is that the Azores would most likely be discovered from, and colonized through the Madeiras, themselves a satellite of the Canaries. They'd almost certainly be part of the same cultural unit, with the same sea-tradition and skills. They'd add to the 'lore' or 'knowledge base' of sea currents and winds substantially, and they'd be part of the same economic unit, which, as I've said, seems to revolve around the Canary Islands as the de facto metropolis.
But eventually, the Portugal current and the Westerlies would be figured out, and you'd go directly from the Azores to Gibraltar. It looks like the Madeiras could make the same direct jump. So that would complicate the economic, political relationships. The Canaries would still dominate, but there would be centrifugalism and political and economic conflicts. The Azores and Madeira have no chance to supplant the Canaries as metropolis. But they'd have enough geophysical options to at least create a running erratic conflict and competition and push for autonomy, or at least more balanced relationships.
Looking at all this, and the prospects for an Ancient discovery of the new world, I would say.... possible, even feasible.
The most likely route would be a trader or explorer ending up in the Northeast Trades, and riding the winds, and the Canarian or South Equatorial Current out to the coast of Brazil.
Going back to the distance Calculator, that's 1500 to 2000 miles from the Cape Verde's depending on where they end up on the Brazilian coast. Now, that's a big trip. But we can posit reasonably that the Canary economic complex is regularly doing ocean voyages between the major Island groups of hundreds of miles, and perhaps in the furthest stretches, almost a thousand miles, and has developed some mastery or knowledge of the winds and currents. So it's not at all out of the question.
The problem, as I see it, is that its a one way trip. Not unless the ancients have perfected sailing against the winds. There's no realistic viable way back. And when I say 'realistic/viable' what I mean is a return route fast and reliable enough that people could plan around it, and the economics of travel or contact would make sense.
Let's go back to the Distance calculator. Assuming landfall somewhere on the northern coast of Brazil. Our hypothetical ancient navigator knows that further north, around the Azores, the winds reverse, the westerlies take over, and he can ride them home. So he starts sailing north, hugging the Coast, making his way to the Caribbean. From there he hops up the Antilles, bouncing across Puerto Rico, Jamaica, Cuba, discovering the Bahamas or Florida, and eventually hitting the westerlies along the American shore. Or maybe he keeps hugging the coast reaching Central America, moving north, eventually discovering the Mayans, and either sailing along the coasts of the Gulf of Mexico or cutting across. Eventually he still gets to Florida and the Bahamas, and from there is finally able to ride the Westerlies and the Gulf current home.
Here's a larger picture of the currents by the way....
The trip out from the Cape Verdes to Brazil is optimistically, about 1500 miles, or somewhere above 50% more than the Canarians longest voyages. That's feasible.
To get home? Somewhere between 7000 and 10,000 miles, depending on the choices made. That's far, far beyond the capacities of the Mariners. The boats would literally fall apart. Assuming that it was done at all, it would take years, astonishing perserverance and immense quantities of luck.
There's a remote possibility that someone might actually get out there to Brazil. The chance of getting back is infinitesimal. And even if someone did make it back.... the rigors of the trip would foreclose any regular Ancient Era contact. At best you'd get some throwaway remarks in ancient tomes about the land to the west.
In a sense, the ancient 'exploration' of the Americas would be no more significant than Hanno's alleged circumnavigation of Africa. Something that was maybe done once but had no consequence, lead nowhere, and produced nothing, except some musty travellers tale.
I'll leave Herzen to pluck a thread and unravel the whole thing. 
