Feel like in my younger daze I could hear and feel every tooth of a ring and pinion when they meshed. Wouldn't call it a rumble but definately a noise.
Any slack in bearings, carrier or pinion, could have gear teeth touching uncharted territory. That could cause a rumble noise.
Changing carrier bearings and going back with original shims shouldn't change mesh and backlash at all. Same goes for changing the rear pinion bearing and using the original shim behind it. It won't change pinion depth.
I would add pinion seal, pinion bearings and crush sleeve to that list. Some 30~40 years ago our local chevy dealer had shims to put between the front pinion bearing and crush sleeve. That allowed for a pinion seal replacement without having to pull the diff apart to replace the crush sleeve. That let you torque the pinion nut back tight and was a lot easier than crushing a new crush sleeve.
Other than the crush sleeve fight, Putting cast iron carrier bearing shims back in when they're thick enough to put preload on the carrier bearings can get tricky. Just use a nylon hammer and don't hit them in the middle.
Clay
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