The first step was to mill the white oak and Spanish cedar to oversized billets and let them season a week or two in the shop. After final milling, I dovetailed the white oak frame by hand (good practice!) and set out to mill the airfoil-shaped support bars.
My biggest problem was getting the dowel-end to be well formed. I got some great advice from the joinery forum about machine approaches, but finally ended up whittling them rough, then bringing them to a final shape with a homemade dowel-cutter formed of a steel plate with three overlapping holes (the overlaps create cutting teeth—sorry, didn’t take a picture). They ended up good enough, I think.