Im not questioning how you are going to achieve the bent angles, youve mentioned steam.
If it were me, (it wouldnt be, because I wouldnt attempt something as difficult), since you mentioned oak.
Couldnt you just take, lets say for example, a piece of 12/4 , maybe 6 inches wide,if the bend is 3 inches wide from end to end, cut a template out, then trace and cut it out on the bandsaw. Cut all the boards first,to the template shape, then fine tune them all together,(sand, plane) lets say 3 boards all 6 inches width.
Then slice off 1/2 inch spindles and each one will be exactly the same since they come off of the same piece of wood, or use one piece for each side of chair, so each spindle on each side is exactly the same?
Am Im totally off the mark, is my idea anywhere reasonable?