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Sorry to steer away from Harley, but have you Horn guys ever tried different flare terminations?  That is, the boundary condition where the mouth and room meet.  I once saw some interesting stuff done on large radio antennas that improved gain (efficiency) or perhaps bandwidth by adding "petals" to the edges of the horn.  Sort of made the mouth look like a daisy.  Perhaps it was to make the transition to low impedance air a little smoother.  Not sure if there are analogs with broadband impedance converters in microwave transmission lines.

Maybe a flare that turns a full 180 degree outward is good enough.  I don't know.  Maybe it is related to the lower cutoff frequency.  I believe you get some odd phase or impedance effects at that transition.  Such flare modifications (stolen from mother nature's flower design) might smooth this out.  If so, could eliminate some crossover components.

jh

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