What you will have to do is this:
Use the fishing line on one side of the badge, work it until you get to one stud.
Then, take out the string, and then start to work the string on the other side of the badge until you get to the other stud on the other side.
Do the same procedure for above and below the studs. You should be left with a thin sliver of intact adhesives only between the two studs. I think you can try to pry the badge off with a plastic butter knife (like one of those cheap Dixie disposable picnic butter knifes) and see if you can get enough space to slip the fishing string in between the studs and begin to cut that remaining adhesive.