The axle shaft tapers have "teeth" that cut into the smooth surface of a new rear wheel hub casting. There is a minimum beginning axle shaft nut torque on Jeep CJs of 250 ft-lbs. For a new hub, this is followed by tightening the axle shaft nut further until you achieve the factory-specified stick-out length of the axle shaft threads (beyond the outer edge of the wheel hub).
Note: I've attached the factory procedure in a PDF for those interested in the Model 20 AMC Jeep CJ axle shaft hub installation:
AMC Model 20 Axle Hub Installation.pdf 120.03KB 67 downloads
See your factory service manual, it will describe this procedure for the Model 15. For the Jeep CJs, I also go into this installation in-depth within my 1972-86 Jeep CJ Rebuilder's Manual (Bentley Publishers). Note the way you take this thread stick-out measurement...
The amount of torque required on the hub nut can include the use of a 3/4" square drive impact socket and a long handle added to a 3/4" drive breaker bar. I have used the handle from a hydraulic floor jack (very carefully!) to gain enough leverage with some installations. Other installs require far less force than this.
It's always about the correct thread stick-out measurement after tightening the nut. Those attempting to achieve the correct thread stick-out length with an impact gun, even a very strong one, may be surprised to find that the impact force is not sufficient to get the hub properly drawn onto the serrated axle shaft taper.
All of this said, the AMC factory recommendation is a new hub casting if/when the hub shows any kind of damage. If you notice, brake work does not require hub removal, and the hub should, ideally, not be removed unless the axle shaft outer bearing requires replacement. Many do get away with hub reuse if there is no damage to the hub taper or axle shaft "teeth". If the hub has spun on the axle shaft, there is damage—the hub must be replaced.
The hub and axle shaft positioning should be marked before the hub is removed. If you cannot or do not want to install a new hub, and the old hub appears okay, align the hub at its original position on the axle shaft. Tighten the axle shaft nut to the initial torque. I take this a step further and use the thread stick-out method to assure a safe installation.
Once you have installed a hub to an AMC axle shaft in this manner, you will understand why Jeep owners who do not practice this method wind up with the hub spinning on the axle shaft's tapered end or, in the worst case scenario, the wheel hub and wheel/tire assembly can come loose!
There are aftermarket "one-piece" replacement axle shafts available for the Jeep CJ 5x5.5" bolt circle hubs. These one-piece shafts have a more conventional outer flange for the wheel studs and mounting the brake drum and wheel/tire assembly. There are several suppliers for these Jeep CJ axle shafts. However, like you share, your Eagle wheel bolt circle is smaller than a CJ Jeep pattern, and the axle shaft lengths are likely different between the CJ and your Eagle. (Inner axle shaft splines may differ, too.)
As a footnote, the key and keyway on the AMC axle shaft are not intended for withstanding the driving torque at the axle shaft. This key is mainly to facilitate the installation of the axle shaft nut in the manner I've just described. (It may provide a very marginal safety factor, but looking at it, you can see that the size of this key cannot withstand axle torque or loads.)
With a new hub, you are actually "cutting" teeth/splines into the smooth hub casting taper as you tighten the axle nut securely. By securely, the only safe and trusted method is thread stick-out length. Any attempt to use a torque figure (other than the starting torque of 250 ft-lbs for the CJ Jeep Model 20 axle shaft nuts) is futile. Actual torque setting can vary from not much past the 250 ft-lbs minimum to the long handle leverage I mention.
Related information: Anyone remember the vintage Volkswagen air-cooled era rear axle shaft nuts and the use of a long leverage bar for tightening? AMC is not alone here. And there are the tapered axle shafts on vintage Jeep, Ford, Studebaker, I-H and Chrysler cars and trucks that require a hub puller to remove the wheel hub and brake drum. If you need that kind of puller for an AMC axle, get pointers from my OTC Hub Tool video, click here.
When Jeep owners do not follow this hub tightening procedure on the Model 20 axle in a CJ, and especially if they run oversized tires, the hub will spin lose. This can cause severe parts damage or even the loss of the hub/wheel assembly.
Check your shop manual for the AMC AWD Eagle. I'm curious what the thread stick-out measurement is for the Model 15...