[catahoula]

But the bridge is then asymmetric in stiffness. ie its stiffer in one dirn vs the other. Ideally need a rear skin so the front and rear skin are the same.

The bridge is not the gantry; it's not under so much torsion. Your analysis shows the X direction is the weak point for deflection by quite a bit. To keep the two columns parallel and resist X deflection, the important part is spacing out the bridge vertically, as far down the columns as possible. A skin surface on the back face is pretty much irrelevant for the loads here. Even a bolted structure with a similar shape would help quite a bit.

Cheers

PS shop is looking great and envy-worthy