If you look at the .4" cartridges that were being wildcatted in the '60s-'70s, like the Centimeter, .40 G&A, .41 . . . what was that thing, with a rebated rim?
Anyway, the test vehicle for those rounds was the Browning Hi-Power.
If Cooper had really had his way, I think the Bren Ten would have been closer in size to the CZ75 and Hi-Power, chambered in a round more like the .40 S&W than the 10mm.
Because the Bren Ten had been initially designed around the .45 ACP cartridge, it was probably no coincidence that when a .4" round was developed for it, the new round was similar in length to the .45.