I don't have great news. I visited my local expert this morning and we discussed it.
This is what I understood it to be although it's complicated. It can be done as a private party transfer if the registered owner goes to an FFL and fills out the proper paperwork with state driver's license, then it is sent to your local FFL. You would need to contact your local FFL to make sure they are willing to do it. The local FFL then fills it out as a private transfer with documentation. it's a matter of everybody agreeing to this and they are on the same page. If you could take possession of the gun out of state and bring it in to your local FFL, that would be OK too. For example, people who move here, guns are exempt from the approved list.
If the gun goes into the DROS system as a normal sale, the model number won't be listed in the database so the transaction can't be completed.
Wish I had better news. FYI model 57's would have to have any S serial number or an N number under about 300,000 to be eligible for C and R, in which case they are exempt.