Hunter, there's a couple things you can do. One, open up your stance but also bring in your bow arm a bit. Imagine forming a T with your body, arms out at your sides, and looking at yourself from above. Let's say your bow arm points at 3 o'clock, your other arm at 9. Instead of 3 o'clock, try pointing at 4 o'clock or in between 3 and 4 instead. Creating more of an angle at your shoulder should give you more clearance. Don't change your arm position so much as to come out of alignment though.
Two, flatten out your back a bit...it should almost feel like you're slightly hunched over. Tighten your ab muscles and tuck your shoulders down. This should also tuck in your chest a bit and away from the string. Lean slightly forward for more clearance.