Great Alastair!
All you are punching me from time to time, as I also had projects to build a poor man's EMG...
And others still less messing but more difficult to design and calculate. And these others are, number one, the best of all: to make a removable attachment to be simply inserted into the rectangular conical horn of my Aeolian Vocalion gramophone to convert it into an exponential horn, with the same size, i.e. not protruding outside (in principle) that improves the sound by means of a much longer sound conduit with slower flare increase ratio, until arriving to the mouth of the horn. It needs to have a rubber tube at the back which goes up into the back conical J connector at the throat of the horn. Then continues in a series of reentrant rectangular chambers (two rectangular conduits) that run back and forward inside the huge rectangular horn, finally going forward and opening to the real horn throat.
The truck is to make the rectangular conduits, narrower than the horn, with reflector panels at the ends, and a final reflector at the b back that seals itself (with silicone flanges at the borders) against the internal walls of the horn. It has to be removable from the front, and use part of the horn walls... I've made many drawings by heart, but haven't yet put the maths into it to calculate the transverse suitable sections.
The idea is to have an attachment at hand, kind of megaphone reentrant horn, that you insert into the horn and improves the response, getting rid of the horrible conical ringing tone we all know so well...
I should scan some of my drawings and put them herein for discussion and general fun and enjoyment!

I have measured the horn with plans to model it in 3D graphic software so I can measure transverse cross sections of the air passages, and give the right angles and dimensions to the reflectors and conduits, so to make it approach the best expo horn that can be fit into the poor metal horn.
Some day I will take my dirty pants and t-shirt, buy some wood, and try it.