Hi,
After paying attention (and learning from it) to some of the work done by Wayne (and others) I found a very interesting Patent (#4,469,921) from Kinoshita, 1984, with a "similar" horn design.
<<Sectoral horn with side walls linear and opening degree or angle of the horn adjusted by the upper and lower curved walls>>The interest of this is that it explains how a type ""shelf"" frequency response of the horn becomes flat and directivity is improved in the necessary frequency band. With a two angle throat for different frequencies.
Nice.