OK, I'm up to speed. What you describe is exactly how a broken axle will act. When you try to turn the broken side, it just turns the broken part attached to the wheel. If you reverse the jack and turn the unbroken side, you are then spinning the spiders and the inner broken axle is turning backwards...but you cannot see that happening until you pop the cover off. In both cases the resistance you feel is the rough edge of the fracture grinding.
I just skimmed through the old tech bulletins. I was looking for other things, but was surprised to find at least a half dozen bulletins just on Lockheed axle problems. Although your problem could be other things, like spiders, pinion, the ring gear...the most likely culprit is an axle.
I'm curious to find out where it broke. With luck, all the metal debris will be away from the center housing, making it easier to clean the tube and replace the axle. If it broke at the inner splines, then the diff carrier will have to come out to get cleaned up.
If your rear end looks like the pictures above (which is how mine looked), I would still lean to fixing the axle with the rear end in place. Removing a rusted, grease caked rear end turns into an adventure in removing frozen bolts. If your's is cleaned up, then it's really a toss up...
John
John