I'd use 1X3 or similar tacked between the sides at intervals to maintain spacing: maybe make them permanent through judicious placement.

I'd then form the inside and outside curves with 3/8" bending Meranti, and then veneer over that with Band-It or similar.

I've done something like it before. The problem was that the thin edges of the sides shouldn't 90 degrees to the flat because when you tilt the sides inward the edge surfaces are not co-planer. A little creativity in sawing out the sides and beveling the edges is necessary (along with some filler