dont know if this will help, but its a few pictures i just snapped to help explain. this first one is the back of my next hickory stave, the wrinkle looking lines being the grain. the pencil line on the right is my centerline, which is drawn on one of the grain marks. it is the true center which i then layout my bow from.
next one is the same stave, showing the grain lines, my center, as well as the lines which mark the width of my limbs. these ones happen to be 2 inches, which i think you could get close to this out of the oak stave
this one is a side view looking down the stave, it shows how thick i roughed it out, and the middle where the handle will be left thicker.
did you peel the bark off the stave with a draw knife? if you did and it gouged the back then you would have to chase a ring after you allow the stave to dry. some bark is easier to read than others, like the juniper. it had lines that were twisted along the log that showed this. if my picture helps to elaborate and you can read the grain, then you will be able to lay your dimensions from the line you make as center, choosing a grain line that avoids the limbs/knots. to see how bad the grain twists just follow a grain line with your eye down the stave from one end to the center, then the same on the other end. personally i wouldnt be afraid of a 45 degree twist, but thats because im stubborn.lol hope this helps and doesnt just help to frustrate you, im simply trying to show instead of writing it, sometimes it is easier to understand.