If this differential is on an F250/F350 your method is correct. These units either have a Dana 80 (usually found in the 350) or the sterling in the other. You can find the ID number on the tag located on the rear cover bolt; or remove the cover and look down the edge of the ring gear. I have seen galled bearing that freeze the axle to the hub. Twisted spines in the spider gears will also cause this problem. An F150 should have a pin or clips that need to be removed internally. Don’t forget to add limited slip additive to gear oil where applicable.