YUP, the rings and run-of-grain are deadly important. Some sort of backing will help to stabilize some of the runout problems. I do lots of layout with a kite string as it gives me a really straight line to start with. I find the middle of the length, and the middle of both ends, and wiggle the string around till it lays about in the middle of the handle. Then, i measure out from that middle/middle mark for 1/2 the handle, and the max width at that point , and the width at the nocks, PLUS SOME FUDGE FACTOR.....draw the widths i want, using a pencil compass, connect everything and walk to the bandsaw.
Remember that WIDTH is stability, and THICKNESS is power. BALANCE is everything.
piper