the back and middle ply just leaving the outside play in tack.
Kerf Bending Wood Parts.mp4
Another option is use two sheets of 1/8 plywood on the curved sectioned and joined to the 1/4 to the flat top and the flat front.

Just a thought.
The little woody I have ( my Avator ) uses only 1/8 plywood for the top and front. 1/8 is ok for a skin, but it did take some hail damage last year.