You were doing really well, up to the point you said that a zero-weight airframe would have no inertia....Ouch that hurt!![]
Inertia depends on mass, which is completely indenpendent from weight. Weight depends from mass, since it's a force represented by the product of mass and the gravity acceleration, but not vice-versa. See a satelitte orbiting the earth. Has it got weight?? No, otherwise it wouldn't be orbiting. Now has it got mass?? Yes, it's composed of matter, and matter has mass. Has it got inertia?? Yes!! Try imparting a rotation motion to it and see if it will stop after you quit applying the force to make it rotate. Momentum conservation law...

OK, since I don't mean any insult to you, just a constructive critic, I will try to correct that. Our hypothetical (although not that hypothetical, this is perfectly possible to be done, but not practical, there's a difference there) zero-weight airframe if had a low mass too, would have a low inertia. Zero inertia, I may be wrong but that is really impossible, even light has got it inertia (NASA is researching laser powered planes....). But I see your point. Zero weight, no center of gravity, since there's no gravity acting on it. So if there is no CG, how can it be critical?? In this situation, the center that comes into play is the center of mass, as someone has already mentioned in this thread. And it radically changes the laws governing flight, I can only thoerize about them based on my limited knowledge.

If the point people here is trying to make is that only careful designed planes will fly, they are wasting their time. Everything moving through air, by displacing it, generates lift. Everything. Now, if that lift is enough to raise the object from the ground is another story, but that lift is there. Ever seem a racing car "take-off"?? I have a pretty good video of one and I can post if anyone wants to see it. Want a more practical example, and easily done at home?? While driving your car, put your hand out of the window, like it was a wing. Go increasing the speed and when you get to somewhere around 45-50 mph, the lift generated it is enough that you don't need to force your arm to be straight. Your hand is "flying". Adjust the lift by changing your hand's AoA (Angle of Attack).

With that said, now that we know that anything will fly, we have to adjust the thing to it's mission. The 3D foamie is perfect for what it does, that is, wild, tumbling, and agile flight at low Reynolds. Try putting a super-critical, super-high Reynolds, laminar flow airfoil on it, and it will lose it's ability to perform it's mission well, because the airfoil that works better in that situation is the flat-plate, leave the super-critical airfoil to critical speeds (approaching the speed of sound) that it's designed to work at. Pick the flate-plate for critical speeds and you get the same situation, the wing won't work for what it's supposed to do. In a super-critical wing that is to create the maximum amount of lift with the minimum of drag possible (high L/D ratio). Will this wing fly in low Reynolds condition? Yes it will, but not as efficiently as it would at critical speeds. Will the flat-plate fly at critical speeds?? Yes, but again not as efficiently as it would on low Reynolds.