Your photo shows an early 1928 differential. The threads are on the drive shaft, not the pinion sleeve. See the link for an explanation. The set up is not compatible with the later configurations. You will need a pinion puller tool to get it apart. The early 1928 370 ring & pinions are not available from the suppliers. You can easily convert it to the later by obtaining a later drive shaft, there are plenty around due to all the Mitchell overdrive installs. You will also need the larger nuts, lock washer, and thrust washer. The suppliers have them. Everything else is the same. The comment about reinforcing support gussets refers to the banjo. The one on the 28's did not have a support casting around the torque tube flange and they are prone to cracking. The later ones have the support.
If you go to the web site of the Santa Anita A's that the link came from there is an entire encyclopedia about Model A differentials.
Good luck with you project,
Tom Endy
http://www.santaanitaas.org/wp-conte...ing-Pinion.pdf