This isn't something I have actually had a chance to try yet, and when I do, I'll update this post. But I think islands as random encounters makes a lot of sense . Although the islands themselves don't move (for the most part), everything around them does, which is kind of the same...?
Note: The islands are only random the first time they are encountered; after that, they are fixed, unless magical.
Here's why I think this ought to work well:
1) This is basically like a dungeon, where islands are really really big rooms. Only the corridors aren't fixed and mapping is tricky. But there will be monsters and treasure and traps in the form of sudden squalls...
2) Magical, enchanted, lost and forgotten isles are a stock in trade of sword and sorcery fiction, as well as myth.
3) Until the 16th Century, there was no Mercator projection (the most common format for modern maps) and older 'Portolan Charts', in use from the 13th Century, were usually restricted to coastal areas, compiled from observations.
4) The unpredictability of currents, wind, weather, etc, means sailing ships in the Age of Sail, even when they were not lost and were entirely aware of where they were, often did not follow an exact route. Especially on the 'high seas' over long distances. And those small variations in route might lead to odd discoveries.
5) In game terms, randomised islands means you can include them without railroading. There is a chance that if they use route A to B, they will encounter X. Like historical explorers, PCs who travel by sea don't know what they might encounter, or where they might end up. The campaign becomes much less predictable. If players actually fully intended to get to B, then this becomes more like a Sinbad tale: their characters really wanted to get to B, but... life. When they eventually do get to B, of course, all the villains will have progressed...
6) The hierarchy onboard ships might be reflected in the level system of some rulesets, especially those that enjoy player character Titles. You might want specialist ones for a ship: Captain, First Mate, Second Mate, Ship's Wizard, Bo'sun, Navigator, Midshipman, Able Seaman, Cabin Boy, etc. As PCs advance, they can climb this hierarchy.
Islands
For the shorelines of islands encountered, see my post Types Of Shoreline. For what's on the island, roll a d8 or choose from below.
1. Lost Civilization. A civilisation thought extinct still rules here.
2. Lost Race. As above, but serpent folk, or tiny cavemen.
3. Ruins. Crete, etc.
4. Wilderness. Predator-filled jungle.
5. Lost Ecosystem. Dinosaurs.
6. Hidden Enclave. Pirate republic. Amazon Fortress. Wizard stronghold.
7. Hunting Ground. On this island, the centaurs call the shots...
8. Haunted. Ghosts of a lost age; related to the first three, above.
Events At Sea
To keep things fresh, alter the 'register' of adventures or encounters, including ideas of different 'magnitudes'. Don't always make everything earth-shattering. There are three categories I think of in terms of events at sea: Mundane, Dramatic or Magical.
Mundane Events
Even fairly mundane events at sea can get pretty life and death fast. And in their own way tense. When becalmed, PCs might play a major role in maintaining morale, preventing mutiny or coordinating repairs. Mouldy food becomes the seed for the next quest. Storms are pretty dramatic and ought to take up a session, in my view, a lot like a battle against an army of elementals (which perhaps it is!), run in much the same way, with specific incidents demanding the PCs' intervention. A whale might prove adversarial. there are pirates, obviously.
Dramatic Events
Some events are naturally going to take up more than a session and prove more dramatic than the day-to-day dangers and hardships encountered. Encountering a pirate is one thing, but what if the pirate pursues? Many critical choices are provoked by this: Run or fight? Continue on route or head for safety? The ships takes damage and must be repaired. A mutiny kicks off (as opposed to threatening to) and PCs must choose sides. An island is encountered unexpectedly. Or wreckage. Or sargasso. Something unusual climbs aboard. Something unusual is already aboard. War breaks out. An enemy ship is found floundering.
Magical Events
See pirate events above: Is the pirate living? Undead? Phantasmal? The Captain is haunted. The ship is haunted. The ship or the Captain is cursed. Officers become possessed. A storm blows the ship through an ancient portal. Some of the crew turn out to shape-changing serpent-folk. Or a walrus revenge squad. Or sharks. Crew rescued from a floundering wreck turn out to be sharks/were-sharks. Etc.
Factions
Ships lend themselves to factional play. there are always at least two factions aboard any ship: Officers and Crew. In addition, the crew will often contain factions of its own. Beyond merely pro- or anti- the Captain, there will be rival leaders, different agendas (such as the 'We should head home now' faction, the 'We should become pirates' faction, the 'Discipline onboard is too severe' faction and the 'Use the map to get the treasure' faction.
These factions won't all agree with each other and who they favour at a given time among the Officers will depend on which agenda the Captain or Officers favour. PCs should be given opportunities to engage in this sort of factionalism, maybe even taking over the ship if they choose to.
Adventure Seeds
Something evil is onboard, as cargo. In the restricted space aboard a ship, horror ensues. Roll a d6:
1. Vampire
2. Mindflayer
3. Giant, psychic crab monster
4. Troll
5. Lich
6. Ooze
Somebody onboard has a map showing treasure.
1. Captain
2. First Mate
3. Faction leader
4. Player character
5. Political prisoner
6. Monstrous prisoner
7. Ship's Wizard
The Captain isn't who he said he was. Who (or what) is he instead? And who else isn't what they seem?
1. Long lost heir to the throne.
2. A banished necromancer.
3. Avatar of the sea god.
4. A doppleganger.
5. A magically disguised serpent man.
6. An agent of the monarch, on a quest to save the realm.
7. A slaver
8. A pirate of high repute.
The Ship isn't what it seems. The PCs have taken passage on a ship headed for stranger seas.
1. The ship flies
2. The ship travels between worlds
3. The ship is alive (and is its own Captain)
4. The ship travels between planets
5. The ship travels across land.
6. The ship travels across ice.