Even if you got a new barrel, you'll need to take it to a verifier to get its classification changed.
I did this with my USC/UMP conversion. Had a local verifier send in the report (Most gun shops or gunsmiths SHOULD have a verifier) Took about a month or so.
ETA
If you do it at a place like Herron Arms or Dlask, they'll likely do the verifier report for you (if you send the gun in).