Install the cage with NO shims, evenly SNUG up the bolts until there's no endplay in the bearings.
Measure the gap where the shims go with feeler gauges.
Once you have that "zero" measurement, add shims equal to that measurement, MINUS the "preload" spelled out in the shop manual.
(Pretty sure the bearings are "preloaded", if NOT and there's supposed to be ENDPLAY, you would ADD shims equal to the desired endpay to the measured thickness.)
At that point, you can measure the gearlash and see if it's "in spec".
If NOT, you move shims from left to right or right to left, as needed, to bring the "gear lash" into "spec".
That's the standard way to set up 'most ANY differential carrier bearings.