To be honest it's sounding more and more like a lash problem between ring/pinion and if it changes depending upon temperature... To check the lash takes feeler gauges and a little wax to see the contact surfaces. I have never bought a diff set that wasn't a "custom" order that didn't need to be adjusted (although never had to shim one either)

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"When the Team Chief said.... You're trapped in a hole with nothing but a goat and a slinky, what do you do? Stubby said, I'm not sure but it won't end well for the goat...." ~(Overheard) Last day, Phase 3, Q Course