I like Bently’s idea too. That’s the elegant way to accomplish the shape but once you get the shape, I would still recommend hammer veneering. It would be very easily done and you would not:
1) be limited to commercially available species in hardwood veneered plywood and
2) have to find raw veneer to match the said commercial p/w.

You have the hide glue. Get some cheap veneer and do a little practising. Once you learn the technique doors will open that will allow you to go places you never thought you could go with veneer.

The early bird gets the worm but its the second mouse that gets the cheese.