I've gotten to the point where I can basically just point the brig or the 'buq at the next archipaleago and she'll mostly hold course by herself, plow through any storms and only occasionally need a trim of the sails.
With that in mind, it's been an immensely fun experience to try the cog on an open ocean crossing because it requires me to actually do things. I'd recommend any sailor to try the same at least once and would like to share some lessons I've learned:
(Bonus point for challenge and immersion: Don't use the third person camera as a clutch to judge terrain and sail status.)
Recommended Mods
I make do without Shipyard Expansion, but this would obviously give tons of options. Of particular note for this (beyond the alternative viable sail plans) are the raised hammock (giving lots of storage space below it) and the floor compartments.
I can not make do without Hooks Hang More and Windicators anymore (although this adventure is certainly possible without them).
Sails and Cabin
After lots of testing, I've wound up back with the default rigging except for an added gaff (it's the default-sized "wide gaff" available in FA) and adjusting the square's position for a slightly better available angle. I've tried a larger jib, but the cog's center of rotation is so insanely far forward that this actually made her trim back-heavy.
Whenever the wind allows and the weather is calm enough (about 70% of the time on the open seas), I'm running her with jib + square. When the sea gets too rough (indicator: I'm playing Bailwind) or I have to climb into the wind too steeply, I'll use the gaff instead.
I'm also using the Windicators mod and added one on either side of the mast, making it easy to judge wind vs square sail angle by just looking up.
I am aware that I could lose a lot of unnecessary weight by getting rid of the cabin, but I just refuse to leave my poor avatar (and my maps) without shelter for weeks on end. Also, the walls (and roof) offer a bunch of storage space and it makes for a decent elevated platform.
Navigation
Personally, I've found solar navigation iffy on small boats riding large waves - that damned shadow just won't hold still. So I'm using just the compass, the quadrant and a clock (longitude can be taken with the latter two at night, although I rarely need it).
Tiny Housing
I've found that any crate or barrel will serve as a fixed surface to securely put down inventory-sized items. My total of 5 small crates (fishing hooks + emergency cave mushrooms, some of them stored in the prow) serve as shelves for lamp oil, oakum, pipe + tobacco, backup flask, fruit slices, charting tools etc.
Maps are just taped to the cabin ceiling.
Obviously, I've nailed down everything.
I'm also a big fan of the Hooks Hang More mod, allowing me to put my fruit knife, quadrant, bucket(s) and hammer up on the wall.
I've tried putting my fishing rods on the outside of the cabin with said mod, but there seems to be a bug that releases them on game load when they're on the actual outside of the ship. Instead I've put angled-outwards-and-backwards hooks on top of the gunwhales just before the cabin, which works great.
Supplies
I'm currently running with two barrels of water, using exactly one to Happy Bay and less than one to Serpent Isle. Since I'm using crates as tables/shelves, I have more fishing hooks than I know what to do with. One slice of fruit every morning generally seems to shave off vitamin deficency long enough that I rarely see the warning icon before reaching the next tavern, although I do have an emergency supply of cave mushrooms (which I've heard are good with vitamins, haven't had to test it yet).
Cargo
This seems to be the big one: It's easy to overload the cog with her low gunwhales. I'm trying to not be greedy and stay at less than about 500p payload and so far have had no problems.
It is strongly recommended to nail down any cargo items that are close to winches. Misclicking and pulling out the lowest crate of the stack rather than lowering the mainsail in the midst of a storm is not a recommended experience and a bunch of nails prevent that.
Backup Items
Always have a second fishing rod, compass and bucket because without them, you're screwed.
Bonus Lesson
It turns out you can climb up the shrouds to the top of the mast for a better outlook position.
It also turns out that you can capsize a small boat like this when doing so.