Time is the issue here...it used to take several months to get an SBR request filled. Now that the ATF has opened an NFA office in Martinsburg, WV, the turnovers are a lot quicker.
It's gonna cost you 200 bucks for the stamp; the paperwork is downloadable from the ATF, and 2 fingerprint cards are easy to come by (1 for the ATF, 1 for the FBI). Getting the CLEO to sign-off is the painful part (setting up a meeting, bullshitting about the 2nd Amendment, etc.), but there's no reason why he can't sign it (legally, he is in no way held responsible for your actions afterwords). And, if he doesn't want to, you have other options open to you (judge, public defender, etc.).
Just be sure to buy the barrel AFTER you get the stamp....Levinworth is a bad place to be, this time of year!
You can swap it out yourself using a vice, a pipe wrench, leather, and basic hand tools (I did my own, and also tapped it for a bfa).
Rob