RE: Strength Exercise for pull
i think rows would be more beneficial than pull ups or pull downs.
you can do them seated with a machine or bent over with dumbbells or a barbell. Also curls and tricep extensions will help with arm strength.
if you have access to a gym spend some time with a trainer even take your bow with you and show them what the motion looks like and they can help tailor a program to fit your needs.
good luck