I actually split into 3 fleets in my game. I found that I didn't need more than 4-5 Galleasses per fleet. Most capitals would fall to that in 3 turns or less, although there did tend to be some that were harder to crack. It was about the same in my other games on Archipelago.
Not sure what all I'm doing differently... promotion saving and insta-heal is mandatory, yeah? Maybe my dedication to getting Triremes everywhere and plundering every single trade route was slowing the AI down. It seemed like they just kept spending their hammers rebuilding Cargo Ships (each of which turned into half a Galleass for me), rather than any sort of fleet.
What you did differently in your game was get everything done much earlier.

Difficulties with taking out AIs compound the longer you get into the game. It is similar in land games where the earlier you can take out those first capitals, the more success you will have. Having Compass by T74 without finishing Liberty even, getting enough cash to buy significant fleets early, and getting culture enough to get Exploration fast were not small advantages, but huge. Extremely well-played to get that done!
Your "30 turns to sweep the map" credo will only work if you get that ball rolling early and you have no extremely hard target capitals to deal with. Later conquest starts will take longer, as the AIs have more units, ships, CS allies with ships, and tougher capitals the longer the game goes. (Enemy CS caravels slowed me down a lot in the late game actually in my try.)
A T89 compass for me and enough cash to buy only 3 galleass' instantly after that turn meant delays in getting the ball rolling. [Despite picking peaceful-type civs, my trade route plunder tally was low early on. The map seemed very strung out, so I'm not sure the distances allowed as many trade routes as there could be.] Tribute and more cargo ship plunder soon got more ships online but the start was already fatally slowed for a quick sweep. It didn't help that the Great Lighthouse was built in the furthest capital from me, with only a narrow arctic inlet for two non-range promotion ships to attack from (while getting slaughtered). Only 2 ranged promotioned ships could attack also, so 4 ships attacking max, 2 vulnerable to cap/composite bow/galleass fire from the capital and surroundings. Could only take it out with 1 fleet just barely after getting ranged promotions and burning up a great admiral to instaheal everybody still alive once. If I was really going for a superfast time, I might have started over after having a decidedly so-so capital and after seeing that hard AI cap, but like RaidandTrade, I could not abandon my shipmates and fought through to the end at T161.
Hats off to you for playing so well, and earning a well-deserved gold medal on this one!