IIRC the 28/20 was based on the 25x194R Hotchkiss AT case and was originally developed in Denmark (?) - the name Larsen comes to mind. I'm sure that there was an item about this in the ECRA Bulletin of a good few years ago.
Aha - found it! It was in the November 1992 issue, a drawing of a 28/20x188R (which looks identical to the German round) from the Rudi Keim collection and info from J.Barlerin of France. He states that it was made by the Larsen company of Otterup, Denmark, for the French Army. It was chambered in a special taper-bore gun mounted on an APX carriage and tested by the Commission de Versailles in January 1940. The cases were provided by Larsen, the projectiles either by Larsen or A-VIS. The first cases were made in Norway. The gun was called in France: "Canon de 20mm Larsen".
That was quite an international project, involving France, Denmark and Norway! I wonder when Germany got involved?
Postscript: I found a response to Barlerin's post by the late Manfred Stegmller, who specialised in squeezebore ammo. He states that the round shown was the 29/20 developed by Schulz and Larsen during 1936-39 for the French Army, using the 25x194R Hotchkiss case as the basis. S&L learned how to make tapered barrels and their ammunition from Hermann Gerlich and his assistant, Hans Neufeldt, who worked in Otterup, Denmark, up to 1934. Neufeldt went to Polte, Magdeburg in 1934 shortly after Gerlich's death, and developed there (at least up to 1935) the ammunition for the sPzB41 in 28/20 calibre. The case and projectile dimensions for the 29/20 and 28/20 are very similar, "the difference being in the curvature".
Stegmller 's conclusion was that the design of the 29/20 cartridge was finished while Neufeldt was still in Denmark, otherwise he never would have used a French case for the basis of the first German taper-bore gun. He comments that most of the projectiles were made by Larsen, with very few made in France. Also, the 29/20 failed and the 28/20 succeeded because Neufeldt introduced the use of tungsten carbide cores (the 29/20 presumably used conventional steel cores).