I saw on that on Realtree Roadtrips. They couldn't get good footage because it was dark. They also used shotguns.

Where I go its legel to hunt them.
Pretty much the same story as ryanaller said, they are ruining a certain place and local game management said they where pleased if we did it with bows.
My first intention was also a fishing rig but although we have a boat, i dont know if thats a smart way.
Canoes would work better maybe but i have no experience in that.
What about using a judo point on a alu shaft. The arrow will come up, right?

It is legal here in sd as long as no lights are used. We hunt them in the spring as soon as the ice comes off the rivers. We use 22s and shoot them in the head. You are correct in saying they do not float for long! I don't know if a fishing set up would hold up to them. They will most likely break or BITE off your arrow if you don't hit them in the neck or head. Good luck and let us know if you get any. I might try it with a bow once myself.
PS: They are most active in the water during early morning and right before dark. You can catch them sleeping in the sun on a bank during the day.

I have a friend that shot one a couple summers ago, took a long while to get it in, he was using a slotted retriever by ams.

To attract them I use bird seed or peanut butter.