In reference to the E-6B wire: The steep angles you refer to actually cause the miles of antenna to be mostly vertical which results in better signal transmission. The wire actually does fly (create lift) and needs to be stalled to hang down vertically, thus the plane flies in a relatively tight circle (30-50 AOB), around stall + 10% to achieve this "verticality."

OBTW...the antenna's diameter is no thicker than your pinky fingure.