Stuck Diff Shim
I know I would get myself in some situation like this too.
Disclaimer: I am not a differential tech so maybe the following is useful, maybe not.
If you have an air hammer, maybe you could vibrate the housing enough to allow you to pull things back out.
No, I am not suggesting using the air hammer on anything critical, but the outside of the pinion case should be "safe" to apply vibration to.
It might take 2 people, 1 on the hammer & you with your hands on the locker / spacer.
To go back in, (assuming you get it out) maybe try the freeze method.
If you put the locker & spacers in the freezer over night, they will be just a tiny bit smaller than at room temperature.
Maybe you thought of it, maybe not.
Just thought it was worth a mention since I have seen it used to get ring gears on the carrier if you put the gear in the oven & the carrier in the freezer.
I am not responsible for any hot water you get yourself into with the wife or girlfriend having these things in the kitchen.

If they're selective washers from the old rear end they might not work.
I never put the ring gear on when I'm setting up side bearings, it makes it a lot easier to handle. Get some washers and get it in tight with the caps on. Set up an indicator and check carrier end play. Pry it back and fourth with a long pry bar and see if you get any movement on the gage, it should read zero. For some reason he doesn't check it, big mistake. Then put the gears in and see where your at. Any shim moves will be simple from then on because you know how much shim each side needs. If they don't have enough preload they will sing to you going down the road
I would ditch the case spreader, it's just going to get you in trouble.





