FFL, being it a smith or manufacturer, checks the gun into his books when they receiver it to show possession of the firearm for repair, repairs it, then sends it directly back to the owner from which they received it (no paperwork required, other than the FLL checking it in and out of there books for the needed paper trail).
Since you are the owner of the firearm, your golden, and is the other end that needs the FFL to temporary receive and posses the rifle during repair instead.
Bluntly, as the owner of the firearm, you are allowed to ship the firearm to your self across state lines without the needed of a FFL.
Its when the firearm is not going to be in the possession/ownership by the owner (shipping in transit is OK when shipping to yourself), that a FLL is needed instead for the needed paper work, which is just his books.