[drolston]

I broke the left axle on my '41 two years ago; just nudged the gas on a level street. Replacing a busted axle took me an afternoon 60 years ago; this time it took a week.

Regardless of which axle is broken, the left axle housing has to come off because the ring gear is on the left side of the differential carrier. The rear end does not have to come out of the car. Get the car up with both wheels off the ground and set both sides of the frame on reliable jack stands. You will need a wheel puller for both sides; the cheap one in my pictures works fine. Then you have to disconnect the left side spring shackles (no spring spreader needed; see photo), shock and radius rod. The backing plate then comes off; the e-brake cable can stay connected but it is best to disconnect the brake line. You will need a floor jack or bottle jack under the banjo to adjust the height as needed to get the axle housing to clear the other stuff. The axle housing is probably stuck to the banjo by gaskets. A couple of good whacks will knock it loose. The gasket is multiple layers and may tear, but if you keep all the pieces you can stick them back in place with grease upon reassembly. It is important to preserve those several layers of gaskets as those layers were used to set the spacing between the ring gear and pinion, and that is a tricky business.

The axles and carrier will slide out the left side if you were smart enough to have left about six feet. The carrier comes apart, the replacement axle goes in. A big vice on the good axle to hold the assembly vertical will make that part easier.
It all goes back in reverse order, easier than I thought. Take the opportunity to inspect the drums and wheel bearings. You may need to replace the grease seals, but do not replace the bearings unless they are clearly bad, because modern replacements are a gamble. Put at least 225 ft-lb on those axle nuts, and then do it again after running around the block a few times.

Good luck!