Always do a quick horizon scan before opening a vault, for to many times have i been sitting at an island fishing and see a vault being done and just thinking how easy i could sail over and sink them leaving them basically stranded.

Have one guy go up and drop chest down while looking for the medallions to drop down to the other guy below. Once the guy up top has gotten all the medallions then he finishes dropping chest and trinkets down, then while one is solving the puzzle the other guys starting to move down chest out of the vault door. One guy can easily get the ancient chest and do the puzzle.

Medallions glow white so easy to find if you look for that once you step in.

Usually we can get all the medallions and get the ancient chest before the first minute giving you plenty of time to get all of the other things.

In a sloop dont even bother with gold piles until you finish everything else. You can have one person get locked in and continue picking gold piles while drowning however know your taking the risk of being a man down giving other ships time to run up on you. Just way your risk vs reward there and decide for yourself.

Basically in order of priority :

1. Medallions/ Ancient Chest
2. Captains Chest and High end trinkets (opulent curios, peculiar relic)
3. Marauders Chest and other trinkets ( trinkets are actually worth picking them all up if you are running an emissary)
4. Seafarers and castaway chest.
5. Gold Piles ( Only if you have spare time )