Buddy,
I would stick one with a broadhead from that bow of yours(and have) before I would take on one with a "rat shooter", especially at 50 or 100 yards. I've killed a half dozen of them, usually incidental to other hunting. The most recent was last year at about 125 yards with the 30-30 savage, first shot must have been close because he turned to fight and the second one just flopped him.
I don't think you'll be that lucky to catch one out in the open very easy. If you do see one it will most likely not be a mature one as the young ones are dumber about getting caught out in daylight in the open.
They tear up a lot of pastures, hayfields, farm terraces and even golf courses digging for ground squirrels, gophers,etc, so yes they are destructive. When more small farms used to have a chicken coop the fox couldn't even hold a candle to a badger when it came to killing chickens.
Good luck with your badger hunting expedition!