A word of caution: the flexibility may be desired by the manufacturer. C-channels are typically used on truck frames to allow flexing. Rigidity increases strain on the components.The cross members pierce the 12" x 16lb I-beams that run the length of the trailer, but the C-channel cross members are only welded to the I-beams along the web of the channel. I'll fix that by welding the flanges as well which will add stiffness to the trailer.
A friend of mine builds convertibles for a few years now and he told me that his first prototype was too wobbly but then his second attempt was too stiff and not driveable. The third version then "felt right".