Another thought, grandpa used to do a lot of woodworking, made hardwood furniture and the like. One piece he made several of was a plant stand. It had a solid round base and a solid round top, and the 3' vertical column was made up of multiple slats, like a 2 dozen that were maybe 1/2" x 2"? Anyways, to make the column he took some heavy fabric, laid it out flat, glued the slats to the flat fabric, and then wrapped the fabric/slat assembly around the solid base and top. Once wrapped around the base/top, he'd then nail/screw it all together. Maybe use the same cloth/slat principal to get the curve around the top of the chest.
damn, thats one of those stupid simple ideas you cant believe you never thought of