From what I've read, the first step in re-assembling the differential is to set the pinion shaft front-to-back, using shims at the head bearing, then set pinion shaft bearing pre-load using shims between the tail bearing and the spacer. The shims at the head bearing fit between the case and the bearing race. Using a drift to remove the race to adjust the shims will damage the shims. Is there a reason why some of those shims could not be placed between the bearing cone and the pinion gear, at the other side of the bearing? Adjusting that shim pack thickness could then be done by removing the pinion shaft from the bearing, and with the race left pressed into the housing.
Thanks, Phil