Diff is blown for sure. You didn't try turning the pinion? With a limited slip like yours you should be able to turn any of the three and have all 3 turn together.
I'm not a big fan of the Belleville washer style clutches. I think this might be the way to go.
Auburn Gear Part 5420112 - Dana 44 H/P Limited Slip
4 years of drag racing to test it out anyway.