Dale, I hope you do convert it, as it has lots of potential (and already won awards).
#1, 2, 3, and 5 sounds good to me.
On #4, I kind of like the auto-trading vessels, but I think there needs to be more depth to the system, especially what drives it. And the AI needs to know how to use it of course too. I get the feeling that Vanilla Civ's AI is way to dumb to use it right, as I only got robbed like a few times. And predicting the generation of vessels seems just plain random to me. And I could park my pirate vessels fearlessly near the enemy. Hmm?
On #4, I'd go for way more resources, and some civ-traits on resources. Like for instance the Native Americans should be able to pull fur out on demand for anyone (and really there should be more fur on the map anyway). Central americans would have odds and ends of silver and gold on demand.
All in all, I'd look to Colonization! as a model to improve the economy some, but I wouldn't completely trash the system in place. It's something of a placeholder, but it can be expanded. Colonization! got about everything right, except for a bit too much micro-management.
Main things I'd like BTS to fix is:
Europe is way too placid with the Christendom thing, yet it should be having lots of orthodoxy wars, and simultaneously explodes way too rapidly in colonization. There should be more tension and strife in Europe which will discourage the type of scattered, hopscotch colonization. The stock marriage events/quests should play into the blood lines of the rulers, and not just be religion diplo. Quests based of Henry the VIII are a must.
Also perhaps mod the diplo effects of religion. Perhaps having a common religion should be decreased in value (less than a 4 mod), and cultural border tensions should be higher? Perhaps as religious schisms develop, if you fail to persecute them from your cities (Inquistor unit anyone?), it will affect your common religion modifier (so no +4 mod, if you passively allow schisms in your cities). Inquisitions of course cost lives, unhappiness, and might promote civil wars and revolts!
The AI doesn't grow it's cities smartly (at least in vanilla Civ4):
I had a pop 23! city about ~ Carolinas, and a size 19 at about Yucatan and Antilles. The AI mostly had 5 to 9 size cities, but tons more cities than me. Clearly the AI is not sharp on growth, and clearly there's not enough tension, and too rapid colonization. The AI notoriously is racing for the nice spots, and then goofing them up by one square, as if to dare you to actually conquer and keep that city.

The BTS AI is much smarter I'd guess.
Massive cultural spread too fast, and colonies survive to easily:
I like how you cut out cheap culture from missionaries conversions, but I think the answer may be to cut the cultural spread of buildings more. And have regular natural disaster events like the blizzards in the Age of Ice mod (of course the events could be diseases, food events, surprise barb raids). Unhappiness or sickness before Astronomy (Ocean trade) should cause the colonies some serious heartaches as they don't have the motherland right next door to help them.
Hopscotching placement of colonies:
Sometimes the AI, in it's believe that more, smaller colonies are best, will try to insert them in the most ridiculous places, as if it thinks it can win some kind of culture war, or open a back door. I'd suggest deterring that by making colony maintenance costs even more for distance. Then to compensate for that, there should be regional colonial capitals (like Viceroy capitals) that mediate the distance maintenance costs to the true capital some. So in other words, perhaps a number of "subordinate" palaces, with the number allowed fixed to the total number of cities in the civ. Perhaps something like 1 subordinate palace for every 3 cities in the civ, with the distance maintenance cost paid based on distance to the closest subordinate palace; That and increase the base maintenance cost for distance.
Movement scale distortion by water. Obviously galleys are too slow, yet they only stay in the med. I though maybe caravels should be 1 tile faster or so. At any rate, perhaps have different speeds for different tile types? Like med sea tiles would be blazing fast, while mid-Atlantic ocean tiles would be relatively slow. I think that should correct for any distortions of travel times.
G'luck!
Okay folks, IF (note I said "if" not that I "will" do it) I were to convert the popular AoD mod to BtS, what changes would you like to see?
I'd like to see the following:
1. Add South America and African West Coast.
2. More Indian city names.
3. BtS piracy (with Pirate Hunters modified to fit).
4. Better trading concept between New and Old Worlds (in other words drop the auto-trading vessels for different method).
5. Start 1418 which marks both the darkest time for France (fall of Paris to the Duke of Burgandy) and the historical beginning of the Age of Exploration (first part of the Age of Discovery) and European colonisation with Portugal's discovery and settlement of the Madeira Islands by Henry the Navigator.