You had the cut down 308 brass and ream it out o make the ammo if memory serves.
The grip was just too long for most to wrap there fingers around, same at the desert eagle.
And that leads us to the real issue, as long as the desert eagle uses regular 44 magnum rounds, the automag rounds will price it right out of the market.
I have a wonderful Ruger three screw blackhawk in 41 mag, the cost difference between the 41 and the 44 is about 2-3 to one in cast pre round.
I think the Automag III was chambered for the .30 M-1 Carbine cartridge. Much less expensive to make than the original, full size Automags. As Ruger also learned, a handgun in .30 Carbine is really, really loud.
I can't see S&W tooling up to make anything like that. With a few exceptions like the SW1911, they have largely abandoned the metal framed semiauto market. So have most buyers.
Like Mr. Robinson said in The Graduate, "Son, the future is in plastic."
You had the cut down 308 brass and ream it out o make the ammo if memory serves.
You could use .30-06 brass also. Been there and done that-once. Starline will occasionally run .44 AutoMag brass and it was available along with loaded ammo from at least 3 companies for a short time back in the day.