I would agree. Round would be stronger. A little harder to work with, but stronger.
I assume you have the capability to aluminum weld and bend the tubing.
Im not sure what is around Great Falls, but we have a steel fabricator/distributer here in town who is SO MUCH cheaper for bulk material of any kind than any hardware store or place the average Joe would go.
I have wondered about making one for my edge as well. I would use atleast 3/4" od or 1" od tubing for the major structural members and 7/16" or 1/2" od tubing for the cross members and any members that would be only for shaping the screen.