Does anyone have any experience with the .44 AutoMag cartridge?  I think it sounds like a neat idea.

Where to get reloading dies?

Maybe rebarrel a FR-8 for it.  
Kind of a "Destroyer Carbine Plus".

Or an AR upper for it?

The .44 Auto Mag cartridge was introduced in the ill-fated Auto Mag pistol in 1971.  Its rimless, straight wall case was formed by reducing the length of the .308 Winchester case (or any other member of the .30-06 family) to 1.30 inches.   The .44 Auto Mag was designed to shoot .429 inch bullets at about the same velocity as the .44 Magnum.  No U.S. manufacturer has offered a factory loading for this cartridge, but cases were once available from a Mexican firm of Cartuchos Deportivos Mexico.

The gas operated Auto Mag featured a rotary bolt with locking lugs located at the front , much the same design as the later Wildey and Desert Eagle autoloader.  Like those two, it was an extremely massive and heavy firearm designed to give handgun hunters .44 Magnum power from an autoloader.  The cartridge was an excellent move in the right direction in the 70's, but the gun was short lived due to a variety of reasons.

Like its ballistic twin the .44 Magnum, the .44 Auto Mag is powerful enough to be used on game such as deer and black bear at woods ranges.  Whether or not one should go to the trouble of doing so today is questionable.  Forming the case requires a set of custom dies from RCBS, an inside neck reamer, and plenty of spare time.  If not for the availability of dependable autoloaders in .44 Magnum and .45 Winchester Magnum, the .44 Auto Mag concept would probably still be a good idea.

Cor-Bon offers loaded ammunition

The AutoMag is not gas operated...it's recoil operated.  I made one AR-15 upper chambered in 44 AMP.

Tony Rumore
Tromix Corp