Jake,

why would curved beams with a tight trampoline help stiffen the platform? You might put some torsional load on the beams, but would that stiffen up the boat?
As long as the warp and weft of the trampoline is aligned across and lengthwise of the boat, the major load path is on the bias of the cloth, so the trampoline will stretch and distort instead of taking up any loads. At least that is my view and understanding of this.
Perhaps you have an applied engineering lesson for meg?