Actually, this is why you need to always drain to infinite sinks, rather than mere overflow or evaporation areas unless you have extremely controlled circumstances.
Bridges actually make a decent "sink", as they pulverize water as well as items. Simply set the bridge to a repeater (possibly even an
ocean-based repeater) to make the bridge constantly smash water. Obviously, this requires non-clogging plumbing (pave with roads to prevent tower caps!) that drains into the bridging room, and larger bridges work faster. Without some method of preventing inflow from an infinite fountain, however, an ocean will always overpower a sink unless you have more sink than fountain.
Alternately, the "classic" method of draining the ocean is to engrave a fortification to the edge of the map (you still need to pave the drain with roads!) although even that will be subject to constant flooding unless you are using progressive layers of pumps to drain deeper into the ocean than it can refill. (Kiss your FPS goodbye!)
Your best bet to reclaim that passage is to dig out several sinks, and then connect them to either end of the passage via digging a ramp up into those areas. For dwarf safety, have them dig diagonally upwards from a (non-lever-linked) doorway or from under a bridge. (
See "exploit from below".)
Since the passage is only one tile wide, if you have infinite sinks connected to either end of the passage, you should be able to drain input that has to squeeze through one tile faster than it can sustain water within a single passage like that if you're draining from both ends.
Also... clean up your boulders. Shame on you.