Problem with owning one could be that our Glorious Leaders likely would have it classified as a 'short-barreled pistol' or as a .32-calibre, both Prohibs.
In the first instance, they are taking advantage of a security name for the Pederson Device. It was called the "Pistol. .30", Model of 1918" for security reasons only, just in case Fritz was listening.
In the second case, the French 7.62mm Longue was an out-and-out copy of the Pederson round and "everybody knows" that a 7.65mm is a .32, even if it isn't.
I do know that Pederson ammunition, 30 years or so ago, still cropped up occasionally and it worked in the French 1935 pistols.
As to making the stuff, I do believe that .30 Carbine casings can be persuaded to do the job. BTW, the Carbine casing also can be altered for the Austro-Hungarian 1907 Roth-Steyr cavalry pistol.
The Pederson Device itself was in essence most of a .30-cal semi-auto pistol which was shaped to fit into the boltway and chamber of the 1903 Mark 1 rifle. Cocking was by means of a "mouse" on top of the thing, which ran back and forth like the slide of a pistol. The barrel part was shaped like a .30-'06 round and filled the chamber. Its forward part was rifled finely and shallowly in order to spin the bullet on firing and THEN allow it to take the rifling of the actual rifle bore. Searing mechanism for the Device was, as already pointed out, incorporated into the trigger mechanism of the M1903 Mark 1 rifles. One estimate has it that there could be as many as half a dozen Pederson Devices in private hands. This tends to put them out of most folks' budgets (including mine!).
Hatcher gives an account of a firing test of one of the things in his famous "Notebook".
Hope this helps.