I started on the Aubrey and Maturin series not too long ago and I've been wanting to game this period too.
I've settled on Blood and Plunder for the moment, and it sounds right for the amount of detail you want too.
There are a few issues though:
1. Its set prior to the Napoleonic age.
2. Its 28mm so it takes up a lot of boardspace.
3. There are usually only 1-2 ships per side, unless you play on a REALLY big board.
4. Currently there's no ships of the line. The biggest is a light frigate with a small Galleon comming out in the spring.
5. 28mm ships are expensive although B&P ships are some of the cheaper (but still good quality) 28mm ships on the market.
Issue 1 could probably be ignored, the naval tactics probably werent all that different for the smaller vessels and their engagements. Issue 2, 3 and 5 could be solved with either a huge board (10+ feet x 10+ feet) or by using 10 or 15mm models.
Issue 4 requires you to make up rules for larger ships, but that I dont think it would be too difficult once you have a grasp of how B&P handles naval combat.
There's some really nice and cheap 15mm pirates miniatures out there, that could easily work as sailors and there's lots of soldiers that would make fine marines. For me it looks like finding 10 or 15mm ships at reasonable prices is the biggest issue.
If you want to stick to 28mm and small engagements, you could probably save a lot of money by only buying some sailor type models from B&P and making your marines from plastic kits. Ships can be scratchbuilt too. Gary Chalk made som wonderful Brigantine plans that can be found here:
http://wargaming.info/2010/arrr-a-buxom-beauty-a-pirate-ship-in-28mm-part-2/#.Wae43shJY-UPart 1 of the blog, which has a lot of details about construction is also worth a read:
http://wargaming.info/2010/avast-ye-lubbers-a-pirate-ship-in-28mm-part-1/#.Wae438hJY-UI havent had time yet, but I intend to build a couple of ships, probably by enlarging Gary's plans a bit to make frigates.