Brian: A couple thoughts.
First, the wall thicknesses of the main frame tubes in a Bensen-syle frame are driven by two considerations, besides their basic load-bearing strength. First is the need for adequate bearing area where bolts and bolt holes pass through the tubes. Second is the simple fact that extrusions have a constant section. The upshot is that the walls are much thicker than they need to be along most of the span of each tube. The only places where the walls NEED to be 1/8" or 3/16" thick is in the vicinity of bolted joints. The holes both reduce cross-sectional area and act as stress raisers.
Second (and contrariwise), a Gyrobee, or similar design having a vertical mast, loads the mast in a different way than a Bensen/Brock. Bensen raked his mast aft, so that the mast is loaded in nearly perfect tension when the rotor is flying at a 10 deg. disk angle of attack. Thus the mast experiences relatively little bending load, at least in cruising flight. 'Bee-class craft, OTOH, intentionally ignore this strategy, partly to accommodate the tall shape of the Rotax fan-cooled, inline engine. As a result, a 'Bee mast is constantly loaded in bending in normal flight. In fact, some numbers I ran long ago showed that a plain 2x2x1/8 mast on a 'Bee would be subject to a constant fore-aft bending load that's a little closer to the limit than most of us would like. Hence the universal (AFAIK) use of either a double 1x2 mast or single 3/16 wall on vertical-mast gyros.
Bending, of course, is greatest near the fulcrom. The hinge of a foldable mast is something of a fulcrum, in that it is typically way stiffer than the tubing above and below it. Moreover, there are bots and holes at the hinge. So, for both reasons of bending strength and restoration of the local strength lost to bolts and bolt holes, the tubing on both sides of the hinge should have adequate wall thickness.
If there were an easy way to thin out the tubing wall in mid-span, away from the hinge and any other bolts, this could be done with no loss of safety factor, but it couldn't easily be done with simple extrusions. Don't go at the tubes with a belt sander!
Those of us who play with sailboats face the same issue with masts -- the cheapest way to make them is with aluminum extrusions, but if you do that and make the mast adequately strong at bending points and bolting points, it's way too heavy up top. But you live with it because building a tapered mast out of aluminum is enormously expensive for the few pounds saved.
This inability to adjust the amount of metal per foot in long-span frame members is one reason why built-up truss construction, as in Vance's Predator, is theoretically more weight-efficient than long extrusions. With very careful design, you can place just enough metal at each station to meet your safety factor, without needless weight. Again, though, the weight saving is modest and must be "weighed" against the much higher labor cost.