I think you can get it CNC routed to basic shape, a little smaller than needed. Then glue and assemble it, dry it to reduce warping, varnish etc and chuck it in a lathe and bore the inner bore to exact dimensions.
You do know that if the veneer is springy and needs to be cranked 5cm down to fit, then it is NOT going to be round even though the outside former is round? You probably need an inflatable bladder or similar to fit inside the veneer and expand it outwards to form a perfect round shape against the former.
What are you making? I've seen drum shells made in a similar way but usually around a round centre former then held with outside bands until the glue sets.