Why does a body submerged in a more conductive fluid still conduct current?

Electric eels tend to curl around the prey when hunting (and shock the predators when these make contact), so the shortest path for the discharge may well be though the prey's body rather than surrounding water.

^{Source: phys.org Credit: Kenneth Catania}

Additionally, electric eels are fresh water animals, so your assumption about water being more conductive doesn't really hold. Blood and lymph are better conductors thanks to the ions (mainly Na\$^+\$ and Cl\$^-\$) present in them. In the end, a significant portion of the current will go through the body, which is enough to stun the prey or scare away predators.

Because the water is not a superconductor. You can model a sea water as a ladder of resistors put in parallel from/to infinity. Now if you apply the voltage difference between two points, the majority of the current will pass at the shortest way, the remaining arround. But exactly how much is a function of the resistance/conductivity of the water. More conductive, then the current cone to the sea bottom would be narrower. Less conductive water, then the current spread would be wider.

^{simulate this circuit – Schematic created using CircuitLab}

Current takes all available paths simultaneously

... in proportion to their conductivity. (conductivity is 1/resistance, and its basic unit is the Siemens. A 100 ohm resistor has 0.01 Siemens of conductivity. Paralleling resistors now gets a lot more simple, you are now simply adding each of their Siemens and turning that back into Ohms.)

If that were not so, your house would never get any power - all of it would go to the steel mill, shopping mall or datacenter across the street.

This is how cows get killed by lightning that struck a tree nearby. Several megavolts at the tree radiate into the earth, creating a voltage gradient of say, 600 volts per metre. That puts about 1000 volts between their front hooves and their rear hooves. Some tiny amount of lightning current also travels through the cow, killing them.