Remove whirlpools and make them an event.
Imagine this:
An even occurs randomly, much like the meteor, spawning whirlpools throughout the map.
Each vortex can only be used once, after which it disappears. After a set amount of time (shorter if the event is more common, longer if not), they all vanish until next event.
Each vortex might lead to a lake, the ocean, or even an underground river. Vortexes will NOT spawn on claimed waters (so people can still claim their lovely landlocked lakes and such).
Bonus: maybe make cave anglers or some other water creature spawn at the destination as well? Could be nice for hunters...