It sounds like you got your answer, but just to add my experience; if the serial number has changed, you will have to fill out all the paperwork again at your FFL, just like when you purchased new. I had to do that with a rifle that Remington replaced last year.
Jeff

I did not have to fill out new paperwork when my S&W rifle was replaced with a new serial numbered lower. Nothing in sec. 922 states that such would be required. Companies obviously have different policies and interpret the law and their own polices how they best see fit at the time.

This February and no.

Only once have I ever had to ship anything back to a manufacturer - a slight mishap with my Ruger P90 that was 100% my fault. I shipped it UPS to them and they sent it right back fully repaired free of charge with a nice handwritten note.