Another suggestion might to go with 3/4" HDO plywood. This is the stuff used to build concrete forms. It's made with solid veneers and manufactured under extremely high pressure. You probably wouldn't want to afford a whole sheet of this for your purpose. That said, it may be possible to get a small scrap piece from a local concrete form contractor. BTW, this stuff also comes in 1 1/8" thickness and is commonly used for those premanufactured form systems. Needless to say, a small piece of that would be bombproof. Also, a plus for using that thicker material might negate the need for additional bracing, particularly in the case of a seat designed with some amount of "frame overhang".