Welcome! I've got no special insight available Eddie, but I guess I had always assumed the noun form was, ahem, a contraction from the description of a contract killer, thus to 'taking out a contract', thus to just 'contract'. But who knows - maybe the journey was the other way - I shall watch with interest.

The use of the verb to hit seems plainer, being a natural extension of other violent movement associated with the word - especially when you think of the French cognate abattre, leading to our word abattoir.