re: Need construction ideas

I like Thorreain’s idea as it looks like compound curves to me as well.
If it were me from there on I would hammer veneer it. It would be a very difficult vacuum bag job because with compound curves the veneer would have to be several perfectly jointed pieces. That’s not hard when hammer veneering. You just lay on one strip, overlap the next, run a knife on the joint line, remove/peel up and remove the scrap and hammer back down. It would be best to use an “underlay” veneer to help eliminate print through of the substrate.
If you go with a flat lamination, hammer veneering is still the best alternative for edges. That way you can match the exotic veneer that should be used on an exotic design like this. I don’t know what is on the one in the picture but it looks. A little like Pao Ferro to me. Something like that would suit the piece anyway.

This is an ambitious undertaking. I’d be using all my wiles to pull it off and I might not succeed. I applaud your quest.