Matt, you must be talking about "Blue Duck", the bow made by John Lee that is a copy of an original bow that Howard made for himself. John told me that Howard made his limbs narrow and deep core for better performance, he liked the limbs to bend into the riser. He also liked a deep and narrow grip.
You mentioned that when you pulled the string side to side as you "started to draw" it felt like the limbs were twisting. To do that you'd have to hold the grip tightly to keep it stationary This limb twisting can be done with many types of bows including recurves. Any attempt to twist the limb is very hard to do as you reach full.
Open the bow hand when you start the draw and let the grip seat itself deep into the center of the hand. Close the fingers lightly around the grip and pull straight back on the string.
If you were driving a car, flying a plane, or a boat and steering with a single joy stick, would you pull the stick from side to side?...I think the tendency would be to keep it centered and controlled. Think of a bow the same way and don't worry about how you could run it off the road... :D
Here's John Lee's Blue Duck, A copy of an original bow made by Howard