To what EmeraldPlay said, I also touched on the idea of an underwater zone in a post of mine.
What I suggested, which would work here, is to have underwater "pockets", and basically discontinuities with old ocean pockets under the Slime Sea. Chasms or caves could have water pockets from before the Slime Sea took over. Temperature and/or salinity differences could cause the Slime Sea to essentially float over these water bubbles. The "safe" aquatic zone/zones would be relegated to contained areas, with the dangerous Slime Sea acting as a ceiling.
With this model, you can completely skip using the Slime Sea as transport. The submarine or chute or teleporter or spring in a cave connecting to a larger network would be self-contained. Travel two and back would be a portal or on rails, so you only have the illusion of freedom of travel.
I think this could work without opening the edges of the map.
If true water travel is ready, then the tether to the mainland could be the "remote power system" or "outside navigational range" or "outside emergency retrieval safety zone" or "technobabble technobabble shock collar technobabble".
The navigation system of the 7Zee Kingfisher Hovercraft it tied to the Ranch's emergency retrieval system. The hovercraft will not allow the rancher to travel too far from the ranch in order to prevent death by inability of the Ranch drones to preform a rescue. Also, the Hovercraft sometimes fills with eels.
And problem solved.
Or....
Better solution, if I can just dream for a minute, go ahead and make the map about ten times larger! :-) Have other islands. Have new zones and biomes, both terrestrial and aquatic. The boundaries of the map can be what your navigation system deems safely traversable. New areas can be added by simply expanding where you are allowed to go. I know this is probably the least popular choice with the devs, so I'll type it in the invisible ink they can't see. :-)