By the time I come to full draw, I try to have my bow pretty much on target, so there are only micro-movements, not really consciously directed, after that. I would have difficulty moving my bow arm after coming to full draw too. For me, being locked in is a good thing. Maybe you just need to get on target earlier in the draw, before you lock in.
I would imagine you could solve your immediate problem by pivoting at the waist rather than trying to move your bow arm, but that kind of gross movement should also be completed by the time you reach full draw. That's not to say that you should never make any movements after coming to full draw. In a hunting situation, you may need to move as the situation changes. However, where the situation doesn't call for it, I think it is desirable to have everything locked down when you reach full draw, so you're shooting from a rock solid platform.