One thought is of stick on sections that were glued together and jointed using a finger type cutter either in the spindle moulder or done on the router.
I'd use a phenol glue for jointing and if done in sections I'd think you could use almost any wood.
Another thought is consider Medite Trycoya and simply rout the entire curved section in one go. It's supposed to be very water resistant but still needs sealing on all cut edges. Just an ides which you could try out over the winter if you could get hold of a small piece. You might find this video interesting:
https://www.youtube.com/watch?v=NvlGamh66bEI don't think a cnc would be any huge advantage if you were thinking of making this yourself Roger. The roof would be interesting to construct.
Have you kept any machinery? or did you sell it.
Mark