Differential troubles

Sounds like something isn't turning in the driveline after the front input and causing it to break. Put the axles up on jack stands and see what turns by hand and go from there.

 

Thats quite special, hope your price was dirt cheap, 2 sets of rears isnt

 

So one is a 2.92 and the other is a 4.33? They must of just scrounged some centers up and threw them in to sell it. Just pull the interaxle drive shaft (jack shaft) and lock in the power divider. Should drive like a single screw to get it were you need to fix it.

 

The ring carrier has a ratio range limit.

 

So keeping in mind that I am not an educated engineer, just an old hack that's failed too many times, I'd do everything possible to not use a spacer.
Reason?: The gear is hobbed from an alloy blend that allows for proper hardening post machining. Usually a form of "case" hardening which is why the hardened gear face can flake off. The carrier is cast from specific metallurgy to accept machining for the bearings and spider poles etc., also to accept the extreme side loading of the pinion trying to repel the ring gear. < is why I would not run a spacer. Each, the carrier and the ring gear are made to expand and contract at near equal rates with temperature. So you have just one mating surface to set the lash proper. If you insert a spacer machined from non-like metals, you now have 2 mating surfaces and the spacer holes ad length to the bolts, which allows more bolt stretch, and under extreme torque input of the pinion, 2 mating surfaces ads twice the opportunity for mating surface slippage.
A proper carrier ratio range should be available for both rotations (the reverse rotation of the power divider head, and the rotation of the rear end), or at minimum for rare model, one end or the other.
There's a place in Washington state "Inland gear" that I have used for rare hard to find stuff.