I played Sea of Darkness some more. In the second half of the game, the major puzzles are getting all the photo scraps, getting the sound depth numbers figured out, and getting all the gears.
Our good buddy Gunnar keeps throwing off my strategies, because he has some photo scraps that you can't get until you visit the hold (after searching Dagny's luggage). Among other things, that means you'll either have to take a second trip to the hold, or you'll have to take a second trip to the pub (to change the tides).
There are thirty things you need to do, and there is no way I can keep track of all of them in my head. So I made a bullet list of everything you need to do, and I ordered them as best as I could. As I said, there are two main routes. Route #1 is "do all the sounding depth numbers before finding Dagny", which isn't so bad. Route #2 is "do all the sounding depth things after saving Dangy". That means you finish the photo scraps puzzle as quickly as possible, but you get slowed down when you need to take an extra trip to change the tides.
It looks like Route #1 is about a minute faster than Route #2, so that's the one I'll use.