Turtle soup tastes great. If you can't bring yourself to believe this, convince others of it, anyways. If enough people eat turtles, which really are tasty from what I hear, catching them will be a plus, since you can at least give them away. They live a long time but breed fairly slowly, so once you have their numbers down, they will stay low.
Find everyone you can that likes to eat turtle, and maybe someone will pay you to bring them back for them. Turn them into money some way or another, and sure enough, you won't see enough of them when you go fishing. Doing a quick search for turtle sales on the internet shows that there is a large market for them.