Member John Thomas or site vendor ADCO. Quite popular request. Depending on what one is paying for the new stripped barrel and the markings on your kit FSB might be the decision maker for me. Brownell's a site vendor should have new chrome lined 1-12 twist barrels with FSB already installed in very near future competitively priced. AR15sport or such already offers a 1-12 twist retro barrel with FSB installed for $239 plus shipping. Other twist rates are also available for less coins.
Always options. Might want to purchase a complete correct appearing barrel assembly for immediate shooting and keep your FSB until you find an authentic Colt LW barrel, possibly stripped on a deal. Can always sell a LW barrel at later date and recoup most your coins. Usually the used Colt FSB will install on a used Colt barrel without a whole lot of effort or skill as they use the same or near same jig in most instances. Figure you will probably tie up $300ish once shipped in a non Colt barrel just to have a Colt marked FSB if someone else does the work for you and will only know it's a Colt FSB if C and Bell marked. Otherwise FSB isn't going to be much different than the rest out there.
$300 should also easily buy a very nice correct Colt barrel IMO especially since you should have the slip ring assembly, gas tube and HG's from kit.