Rear Axle

If you have 1" of play, you have bigger problems. All of the end play is taken up by the one adjuster. The axles butt up to each other through a small button inside the differential. You would have to pull the pumpkin out to see it. Might be able to see it with a flashlight looking down the axle tube with the axle removed.

This will apply if you have an early style suregrip. In the early style sure grip (also call the dana powerlock) which you car would have came with (if it had a sure grip) has a two piece button unit held together with a small pin. My bet is the pin has broken and the two pieces have fallen into the bottom of the diff housing. If you look in the differential where the axles go in the splines and see a 3/8" hole through to the other side, the button has fallen out and are sitting in the bottom of the housing. You can fix them with a roll pin. Or if you don't have them I think they are still available from mopar. I can get the part number if that is the case.

Other unlikely possibilities are: axles too short, or backing plate/bearing retainer/bearing not fully seated into housing.

Hope this helps. If you need anymore help trying to figure this out ask away.