Make sure to use a well known engraver, one that does NFA engraving, then call them if you have to.
No, you don't need a 5320 to mail an SBR for work to be completed on it.
Yes, NFA toys need to be engraved.
Tar Heel State Firearms does a ton of NFA engraving. They are cheap, fast, and knowledgeable about NFA engraving. I personally wouldn't use anyone else.