I'm not sure where the arched half-tube girders you mention would run, but I agree that a lot of the forces try to flex the pack front to back. This might be dealt with in part by running longitudinal raised ribs from top to bottom near the left and right edges of the frame, placed so as not to interfere much with the packbag or body. This would add a lot of stiffness to a plate-like frame. The more arch there is in the frame, to a point, the more this flex issue tends to take care of itself, but there are obvious limits. Also, the fact of the wings extending forward can be used, by bracing them somewhat up along the pack (think triangular wing with the narrow point towards the belt buckle) to increase the longitudinal stiffness of the frame in the front-back dimension.
The hips have a complex set of motions, and they run somewhat counter to the shoulders. This puts vertical loads into a pack that would, for illustration, tend to collapse a simple rectangular frame into a trapezoid. There is also a rotational moment around the vertical axis of the pack, with force translations on many vectors through those extremes. I'd think any designed-in motion around the hips and shoulders would tend to be desired not in the front-back frame flex direction but in the rotation about the vertical axis and one-hip-contralateral-shoulder-up-other-down modes.
The lowest-material way to cut the tendency of a rectangle to collapse into a trapezoid is to connect the opposite corners with a rigid element, a payoff of triangulation. Because we use something related to a flat plane for a frame in order to make room for a packbag, there are some constraints on containing the rotary forces (arches in the plane would help), but I'm thinking that triangulation from the lower corners to some central point or points along the lumbar region would be the lowest-material way. An idea of the lines of stress might be had by putting a fold-prone semi-resilient material on a torso and watching where folds tend to point when walking. My guess is you'd tend to see them running in a fan shape from the hips into the lumbar much as the muscles in that region do. Adding a rib onto a basically planar frame along those lines of force would seem to increase strength and stiffness in those areas as well...I think I'm probably talking about something similar to Dale's girders here.
Laying up hollow ellipsoidal tubes like a balloony composite bicycle frame would garner a lot of strength from the tubular structure in a material-efficient way by enclosing more space, but seems like it would be a fair amount of extra work and it still might be desirable to flatten the tubes in certain areas, e.g., to get the pack frame closer to the back or to provide more arm clearance. Also, I don't think we'd be twisting most of our tubes very much as those on a bicycle might be twisted, and I think offhand that that twisting force is why the bicycle frame members majorly benefit from enclosing a space with a skin. Aircraft wings, on the other hand, tend to have spars to take the levering force of the wings, rather than trying to get most of the strength in that direction out of skin strength. which would require more material. So if your forces are largest in a plane, a rib in line with the force can be the lowest-material way.