AFAIK, the 9mm Red Nine 1920 reworks were part of the original 150,000 Mausers made in 9mm Parabellum, cut down because, as you say, the C96 was specifically banned by the Allied control commission. (I have no idea why they considered what was even then an obsolescent pistol such a danger, but I guess it was a bit like the current "assault weapon" nonsense!) The two I have seen still had the original Red Nine grips.
The book shows one with the Red Nine grips then says that 7.63mm guns were reworked. But the German army never issued the C96 in other than 9mm, though some may have been purchased by officers or individual soldiers. The Austrian army might have bought some, also.
AFAIK, the "Luger barrel" pistol was never a factory or official product. I have never seen one outside that book and pictures copied from it. I think it was probably a "one-off" or at least a "very few off" job, maybe even a gunsmith job.
As to Pate's comments on the reason for the Red Nine, I have to wonder about his assertion that there were a "large number" of C96 pistols in 7.63mm caliber in the German armed forces. That is almost certainly not correct; the Germans never adopted the C96 in 7.63 caliber, and no 7.63mm ammunition was issued. There might have been confusion if officers and soldiers knew of the Mauser and assumed any "broomhandle" was in 7.63mm, but even if they did, they would not have access to 7.63mm ammunition unless they were able to find a local gun store and buy it.
Nor do I know what "results" would occur from firing 7.63 ammo in a 9mm Parabellum pistol, except that the gun wouldn't work and accuracy would have been somewhat lacking.
Until I see some C96 pistols in 9mm with the proper sight, markings, and serial number range with the correct original grips and a "local armorer" Red Nine, I will continue to believe that those grips were marked at the factory, not crudely burned in by unit armorers or made from standard grips in someone's basement.
Jim