Not meaning to be disagreeable, but going through the dealer with a manufacturer warranty item is a waste of time. It's faster and easier to go straight to the OEM yourself.

Secondly - it's common for folks to confuse the rules for shipping firearms for private transfers with the rules for any other firearm shipping, HOWEVER: When sent to the manufacturer for repairs or other work, no FFL transfer is required, for any firearm type. The only way an FFL will "need" to get involved will be if they have to replace the firearm with a new one, at which point they won't be returning the same firearm, but rather replacing it with a different one, and an FFL will have to perform that particular transfer. Otherwise, warranty work goes straight to the OEM and straight back to your doorstep.